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Graphing Inequalities Worksheets (Single Variable)

Solving inequalities worksheets.

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Inequalities Worksheets

Are you looking for free math worksheets that will help your students develop and master real-life math skills?  The algebra worksheets below will introduce your students to solving inequalities and graphing inequalities.  As they take a step-by-step approach to solving inequalities, they will also practice other essential algebra skills like using inverse operations to solve equations.

Solving Inequalities Worksheet 1 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 1 RTF Solving Inequalities Worksheet 1 PDF Preview Solving Inequalities Worksheet 1  in Your Browser View Answers 

Solving Inequalities Worksheet 2 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 2 RTF Solving Inequalities Worksheet 2 PDF Preview Solving Inequalities Worksheet 2 in Your Browser View Answers

Solving Inequalities Worksheet 3 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 3 RTF Solving Inequalities Worksheet 3 PDF Preview Solving Inequalities Worksheet 3 in Your Browser View Answers

Solving Inequalities Worksheet 4 – Here is a twelve problem worksheet featuring one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 4 RTF Solving Inequalities Worksheet 4 PDF Preview Solving Inequalities Worksheet 4 in Your Browser View Answers

Solving Inequalities Worksheet 5 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 5 RTF Solving Inequalities Worksheet 5 PDF Preview Solving Inequalities Worksheet 5 in Your Browser View Answers

Graphing Inequalities Workheet 1 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  on a number line. Graphing Inequalities Worksheet 1 RTF Graphing Inequalities 1 PDF View Answers

Graphing Inequalities Workheet  2 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  and “ -x > 2″  on a number line.  Be careful, you may have to reverse one or two of the inequality symbols to get the correct solution set. Graphing Inequalities 2 RTF Graphing Inequalities 2 PDF View Answers

Graphing Inequalities Workheet  3 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition inequalities such as   “x + 5 > 7”. Graphing Inequalities 3 RTF Graphing Inequalities 3 PDF View Answers

Graphing Inequalities Workheet  4 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition and subtraction inequalities such as   “5 + x > 7”  and  “x – 3″ < 21”. Graphing Inequalities 4 RTF Graphing Inequalities 4 PDF View Answers

Graphing Inequalities Workheet  5 –   Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition inequalities such as   “2x + 5 > 15” . Graphing Inequalities 5 RTF Graphing Inequalities 5 PDF View Answers

Graphing Inequalities Workheet  6 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition and subtraction inequalities such as   “2x + 5 > 15”  and “ 4x -2 = 14. Graphing Inequalities 6 RTF Graphing Inequalities 6 PDF View Answers

Absolute Value Inequality Worksheets (Single Variable)

Absolute Value Inequality Worksheet 1 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are one-step inequalities with mostly positive integers. Absolute Value Equations Worksheet 1 RTF Absolute Value Equations Worksheet 1 PDF View Answers

Absolute Value Inequality Worksheet 2 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.   These are one-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 2 RTF Absolute Value Equations Worksheet 2 PDF View Answers

Absolute Value Inequality Worksheet 3 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 3 RTF Absolute Value Equations Worksheet 3 PDF View Answers

Absolute Value Inequality Worksheet 4 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities that can get quite complicated.  A nice challenge for your higher-level learners. Absolute Value Equations Worksheet 4 RTF Absolute Value Equations Worksheet 4 PDF View Answers

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20 Comments

This web is good

Thanks for your support.

i like it. Its very helpful.

I appreciate the feedback. Good luck with your math endeavors!

I like this website. It is very helpful for students.

Thanks. I’ll be adding more worksheets soon.

Interesting questions. Very good.

Thanks. I’m glad you enjoyed them.

This is a great site! Thanks so much for helping me teach this concept to my 5th graders!

Mr. Colwell

I’m glad that I could help. Thanks for visiting the site and come back often!

Kaity Fanara

Very helpful, thanks!

You’re very welcome. I plan to add some Graphing Inequalities Worksheets soon. Thanks for your support.

c’moon! so easy give me something like, ( m-2 ) x2 – (m+5) x + m-8 = 0, if it has 2 equal roots, what’s m? i need this kind, where can i find

That’s a pretty good one. Let me see what I can do.

Mr. Lindugani Mlilile

Thanks for your website which helps me teach my students of form one in Tanzania. I always teach my students on how solve the topic of inequality. Please add more topic so that my students will continue to enjoys!

It’s nice to hear from our international visitors. I’m always adding new content. Check back often!

It is helpful but I can’t see the answer sheet for all of them.

wish their was some fractions inequalities and equalities

however work sheets have helped me tremendously just the one little flaw of not having fraction problems.

I LOVE THIS WEBSITE. I USE IT EVERY DAY TO STUDY FOR TEST OR QUIZ FOR SCHOOL.

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Inequalities Worksheets

Teeming with adequate practice our printable inequalities worksheets come with a host of learning takeaways like completing inequality statements, graphing inequalities on a number line, constructing inequality statements from the graph, solving different types of inequalities, graphing the solutions using appropriate rules and much more for students in grade 6 through high school. Solutions to inequalities are infinite and are presented as an interval. Kick-start practice with our free inequalities worksheets!

» Translating Inequality Phrases

» Compound Inequalities

» One Step Inequalities

» Graphing Linear Inequalities

» Two Step Inequalities

» Absolute Value Inequalities

» Multi Step Inequalities

» Quadratic Inequalities

Completing Inequality Statements

Completing Inequality Statements

Tackle this batch of printable inequalities worksheets by plugging each of the four options in the inequality statement. Grade 6 students circle all the possible values that make the inequality statement true.

  • Download the set

Graphing Inequalities | Easy

Graphing Inequalities on a Number Line

Graph the inequality on a number line by drawing a circle over the number. Fill it if the inequality has a ≥ or ≤, leave it unfilled if it has a > or <. Draw a line toward the right, if the solutions are greater than the number and toward the left if they are less.

Writing Inequalities from Number Lines | Easy

Writing Inequalities from Number Lines

Study the graph, and construct the inequality that best describes it. Grade 7 students look for open and closed circles, watch for the direction of the line and build an inclusive or strict greater than or less than inequality in no time.

Identifying the Solution Graph

Identifying the Solution Graph

If buffing up skills in solving and graphing inequalities is on your mind, then these printable inequalities worksheets should be your obvious choice. Students choose the graph that best describes the solution for each single variable inequality.

Identifying Inequalities from Number Lines

Identifying Inequalities from Number Lines

Observe the graph in these pdfs keenly and construct an inclusive inequality with a closed circle or a strict one with an open circle. Students in 7th grade and 8th grade use < if the line extends toward the right and > for a line stretching toward the left.

Identifying Solutions in Interval Notations

Identifying Solutions in Interval Notations

Draw logical conclusions, whether the interval with a bracket or parentheses is the right solution to the inequality. The task in these pdfs for grade 8 and high school students is to choose the correct interval notation that best describes each inequality.

Translating Inequality Phrases Worksheets

Translating Inequality Phrases Worksheets

Primarily focusing on reading phrases and converting them into algebraic inequalities, these printable worksheets are sure to give students an insight into comprehending inequalities and their real-life connection.

(12 Worksheets)

One Step Inequalities Worksheets

One Step Inequalities Worksheets

Are you looking for a variety of exercises to introduce or recapitulate one-step inequalities? Then be assured you are in the right place. With a host of pdfs for your 6th grade students to choose from, there'll be no dearth of practice material.

(51 Worksheets)

Two Step Inequalities Worksheets

Two Step Inequalities Worksheets

Refine your skills in solving and graphing inequalities in two simple steps. Grade 7 students separate the like terms on either side of the inequality. Use inverse operations to isolate the variable and solving the inequality will be duck soup.

Multi Step Inequalities Worksheets

Multi Step Inequalities Worksheets

Work methodically toward solving and graphing the multi-step inequalities. With the adequate practice provided in these worksheets finding solutions to multi-step inequalities will no longer be a hard nut to crack for your students in grade 8.

(45 Worksheets)

Compound Inequalities Worksheets

Compound Inequalities Worksheets

Whether you are looking for inequalities that are joined together by the conjunction "and" or "or", these worksheets on inequalities beef up practice and prepare high school students in solving and graphing such inequalities.

Graphing Linear Inequalities Worksheets

Graphing Linear Inequalities Worksheets

Visualize the inequality on a graph, analyze the properties of the line, observe the graph and figure out the inequality, sketch the inequality graph are some exercises present here to challenge your high school students.

(24 Worksheets)

Absolute Value Inequalities Worksheets

Absolute Value Inequalities Worksheets

What happens when two important concepts absolute value and inequalities merge? They create an interesting topic absolute value inequalities. Surge ahead in solving the absolute value inequalities featured in our printable inequalities worksheets.

Quadratic Inequalities Worksheets

Quadratic Inequalities Worksheets

Inequalities involving the second degree taking precedence in these pdfs. Solve the quadratic inequalities, find the intervals that make the inequality true, graph the inequality by sketching the parabola are some exercises included here.

(18 Worksheets)

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Inequalities Worksheets

The pages below all have printable algebra worksheets for teaching students to solve and graph inequalities. Topics include basic single-variable inequalities, as well as, one-step, two-step, and compound inequalities.

Inequalities Worksheets

Introduction to inequalities. Solve and graph the inequalities with only one variable. Students graph the inequality. They do not need to perform any steps to isolate the variable. (example: a ≥ 7)

These inequality worksheets have one variable in each problem. Students need to isolate the variable using only one step. (example: 12 - x ≤ 8)

This page has very basic worksheets to help students identify dependent and independent variables, evaluate algebraic expressions and solve for variables in equations.

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Home » Worksheets » The Best Teacher-Approved Solving Inequalities Worksheets

problem solving inequalities worksheet

The Best Teacher-Approved Solving Inequalities Worksheets

Are you looking for a high-quality worksheet on solving inequalities? If so, Teach Simple is the best starting point. Inequalities are a challenging topic in mathematics, particularly because there are statements where two unequal values. In solving inequalities, a student must look for all values of the variable that make the inequality true. It is a skill that takes time to learn, and that is where the inequalities worksheets come in.

At Teach Simple, we have professionals behind our worksheets. Our teaching materials follow the education standards of the USA, UK, Canada, and Australia, so you can be sure your students will learn government-approved content. All our learning materials are created by educational experts with several years of experience in the education sector. The materials are user-friendly, engaging, attractive, and effective.

Table of Contents

Things to look for when choosing worksheets for solving inequalities, examples of worksheets for solving inequalities, where can you find online inequalities worksheets, benefits of paid vs. free worksheets, why choose teach simple for your solving inequalities worksheet.

When you are looking for worksheets on solving inequalities, there are a few things that you will want to keep in mind, including:

Make sure the worksheets you choose are of high quality, meaning they should be well-written and free of errors. A worksheet with errors cannot help a student learn; it can only worsen their situation.

The students’ age

Make sure the worksheets are appropriate for the level of the students. Some worksheets are for kids in grades 1 and 2, while others are for students in grades 7 up to 12. You can’t give a very simple or very difficult worksheet to a student. This can make them lose interest in learning. Additionally, the worksheets should be interesting and engaging.

The worksheet you chose should be clear and concise. This is particularly important when dealing with word problems. The statements should be clear so a student can understand them and form the inequalities before graphing them. Furthermore, the worksheets should not be confusing but easy to understand and use.

Solving Inequalities – Leveled Checking Worksheet By Eight Gone Sideways

Solving Inequalities Worksheet

The leveled checking worksheet was designed by Eight Gone Sideways for grades 9, 10, 11, and 12. It has four sets (A, B, C, and D), each with three questions, and there is also an answer bank. The students are supposed to complete the problems in sets A and B and then match their solutions with what is on the answer bank.

Set C has proposed answers, and the students are supposed to determine whether the answers are correct or not. In the last set, the students are supposed to work through the problems and show their steps.

Solving 2-Step Inequalities MAZE Activity By The Math Cafe

Solving Inequalities Worksheet

Solving 2-Step Inequalities MAZE Activity is a fun worksheet for 7th-grade students. Authored by The Math Caf, these worksheets have word problems that lead to inequalities like px + q  r or px + q > r, where x is a variable and p and q are rational numbers.

The students are also required to graph their inequalities and interpret them in the context of the word problems. This resource has an optional workspace for students and answer keys.

Inequalities Task Cards By AlwaysLearning

Solving Inequalities Worksheet

Just as the name implies, these are printable task cards that you can print and laminate for durability. The cards are designed by AlwaysLearning and can be used by individual students or in a group setting with small groups, of course. The inequalities on the task cards are to be solved graphically, and there is an answer key and recording sheet.

Equations and Inequalities 6th Grade Worksheet By TheBrightestKid

Solving Inequalities Worksheet

This inequalities worksheet is designed for sixth-grade learners. The author, TheBrightestKid, included 19 pages of problems for the students to solve. After solving, the student will select matching solutions from a given set of solutions. And if their answers don’t match, they will have to identify their mistakes and rework the problems.

St. Patrick’s Day Inequities Activity By Have Fun Teaching

Solving Inequalities Worksheet

St. Patrick’s Day Inequalities Activity is an interactive worksheet created with grades 1 and 2 pupils in mind. The worksheet was created by Have Fun Teaching and is guaranteed to keep your kids busy. The worksheet dwells on numbers less than or greater than.

Graphing Inequalities in Two Variables (Spring) By Peter Jonnard

problem solving inequalities worksheet

This resource comes in the form of Microsoft Word worksheets that you can download and print. You can use them with your students in grades 7, 8, and 9. These worksheets focus on the graphing of inequalities. The best part of it is that it comes with an answer key. Graphing Inequalities in Two Variables (Spring) is authored by Peter Jonnard.

Solving 1 and 2-Step Inequalities: Notes, Practice, and Partner Activity by The Math Cafe

problem solving inequalities worksheet

The Solving 1 and 2-Step Inequalities worksheet is intended to teach grade 7 students number system standards. The sheets are to be used by pupils who already know how to solve 1- and 2-step linear equations.

Note that the sheets do not have instructions on solution steps, except for division by negative numbers. The Math Cafe created the sheets, which are excellent for teaching students how to work with word problems that lead to inequalities.

Systems of Inequalities: Guided Notes and Homework Set By Eddie McCarthy

problem solving inequalities worksheet

Systems of Inequalities Guided Notes are created by Eddie McCarthy. There are five editable PDF files in this package. It also includes guided notes, an answer key, and homework.

If you are a math teacher in grades 9, 10, 11, and 12, these worksheets are for you. The sheets teach math skills, and the guide notes will allow them to learn the skills and apply them. The homework sheets aid in further understanding algebra.

Graphing Linear Inequalities: Guided Notes and Homework Set By Eddie McCarthy

problem solving inequalities worksheet

Graphing Linear Inequalities: Guided Notes and Homework Set is created by Eddie McCarthy for grades 9–12 students. The worksheets are supposed to teach graphing of inequalities, and there are guide notes that make things very easy. This package also comes with an answer key and homework for further understanding of the topic.

Visit the Teach Simple website for the highest quality worksheets for solving inequalities. Some worksheets are available on other websites, but you have to check their quality before downloading and using them.

If you are looking for solving inequalities worksheets online, you will find quite a number of them, some free and some not. However, not all of these worksheets are created equal. Some are of much higher quality than others. In general, paid worksheets are better than free ones for various reasons.

Paid worksheets are of much higher quality than free ones because they are usually created by experienced educators who know how to create effective learning materials. The paid version also includes various problems for solving inequalities for your students to practice with. This can help them better understand the concept.

Paid worksheets will provide your students with extra practice. If your students are having difficulty understanding inequalities or need more practice to master them, using a paid worksheet is your best option. This can be especially helpful if you find that your students are struggling with particular types of problems.

Paid worksheets can help keep your child motivated because they are engaging and attractive.

The main reason why you should choose our worksheets for solving inequalities is that they are of the highest quality. This is because experienced educators create them. Our worksheets are also affordable. We believe that everyone should have access to high-quality educational resources. Teach Simple also offers a 100% satisfaction guarantee and an unlimited download subscription model. Once you subscribe to our site, you can download all the teaching materials you need.

Contact us today to learn more about our solving inequalities worksheet and how Teach Simple can help you achieve your goals.

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Diana R. has over 30 years of experience as a middle school teacher and college professor. She holds a Doctorate from the University of California and has spent 15 years as an academic professor and teacher in the sciences, health, medical, technology, and business fields

We have a lot of interesting articles and educational resources from a wide variety of authors and teaching professionals.

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Last Updated on July 17, 2023 by Teach Simple

problem solving inequalities worksheet

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The worksheets given here require students to solve inequalities in the regular way and also on the number line. Some of the questions ask you to find the inequality variables’ values.

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Solving Inequality Word Questions

(You might like to read Introduction to Inequalities and Solving Inequalities first.)

In Algebra we have "inequality" questions like:

soccer teams

Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

  • Read the whole thing first
  • Do a sketch if needed
  • Assign letters for the values
  • Find or work out formulas

We should also write down what is actually being asked for , so we know where we are going and when we have arrived!

The best way to learn this is by example, so let's try our first example:

Assign Letters:

  • the number of goals Alex scored: A
  • the number of goals Sam scored: S

We know that Alex scored 3 more goals than Sam did, so: A = S + 3

And we know that together they scored less than 9 goals: S + A < 9

We are being asked for how many goals Alex might have scored: A

Sam scored less than 3 goals, which means that Sam could have scored 0, 1 or 2 goals.

Alex scored 3 more goals than Sam did, so Alex could have scored 3, 4, or 5 goals .

  • When S = 0, then A = 3 and S + A = 3, and 3 < 9 is correct
  • When S = 1, then A = 4 and S + A = 5, and 5 < 9 is correct
  • When S = 2, then A = 5 and S + A = 7, and 7 < 9 is correct
  • (But when S = 3, then A = 6 and S + A = 9, and 9 < 9 is incorrect)

Lots More Examples!

pups

Example: Of 8 pups, there are more girls than boys. How many girl pups could there be?

  • the number of girls: g
  • the number of boys: b

We know that there are 8 pups, so: g + b = 8, which can be rearranged to

We also know there are more girls than boys, so:

We are being asked for the number of girl pups: g

So there could be 5, 6, 7 or 8 girl pups.

Could there be 8 girl pups? Then there would be no boys at all, and the question isn't clear on that point (sometimes questions are like that).

  • When g = 8, then b = 0 and g > b is correct (but is b = 0 allowed?)
  • When g = 7, then b = 1 and g > b is correct
  • When g = 6, then b = 2 and g > b is correct
  • When g = 5, then b = 3 and g > b is correct
  • (But if g = 4, then b = 4 and g > b is incorrect)

A speedy example:

bike

Example: Joe enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Joe completes the race in less than 2½ hours, what can we say about his average speeds?

  • Average running speed: s
  • So average cycling speed: 2s
  • Speed = Distance Time
  • Which can be rearranged to: Time = Distance Speed

We are being asked for his average speeds: s and 2s

The race is divided into two parts:

  • Distance = 25 km
  • Average speed = 2s km/h
  • So Time = Distance Average Speed = 25 2s hours
  • Distance = 20 km
  • Average speed = s km/h
  • So Time = Distance Average Speed = 20 s hours

Joe completes the race in less than 2½ hours

  • The total time < 2½
  • 25 2s + 20 s < 2½

So his average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h

In this example we get to use two inequalities at once:

ball throw

Example: The velocity v m/s of a ball thrown directly up in the air is given by v = 20 − 10t , where t is the time in seconds. At what times will the velocity be between 10 m/s and 15 m/s?

  • velocity in m/s: v
  • the time in seconds: t
  • v = 20 − 10t

We are being asked for the time t when v is between 5 and 15 m/s:

So the velocity is between 10 m/s and 15 m/s between 0.5 and 1 second after.

And a reasonably hard example to finish with:

Example: A rectangular room fits at least 7 tables that each have 1 square meter of surface area. The perimeter of the room is 16 m. What could the width and length of the room be?

Make a sketch: we don't know the size of the tables, only their area, they may fit perfectly or not!

  • the length of the room: L
  • the width of the room: W

The formula for the perimeter is 2(W + L) , and we know it is 16 m

  • 2(W + L) = 16
  • L = 8 − W

We also know the area of a rectangle is the width times the length: Area = W × L

And the area must be greater than or equal to 7:

  • W × L ≥ 7

We are being asked for the possible values of W and L

Let's solve:

This is a quadratic inequality. It can be solved many way, here we will solve it by completing the square :

Yes we have two inequalities, because 3 2 = 9 AND (−3) 2 = 9

So the width must be between 1 m and 7 m (inclusive) and the length is 8−width .

  • Say W = 1, then L = 8−1 = 7, and A = 1 x 7 = 7 m 2 (fits exactly 7 tables)
  • Say W = 0.9 (less than 1), then L = 7.1, and A = 0.9 x 7.1 = 6.39 m 2 (7 won't fit)
  • Say W = 1.1 (just above 1), then L = 6.9, and A = 1.1 x 6.9 = 7.59 m 2 (7 fit easily)
  • Likewise for W around 7 m

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Solving Linear Inequalities Worksheets with Solutions

Solving linear inequalities is a foundational skill that you will build throughout your studies of elementary and high school algebra. While it isn’t the hardest concept you will encounter in the entire class, there are a few tips and tricks you should get used to. And the best way to do that is by practicing! 

That’s why I put together this collection of solving linear inequalities worksheets! Let’s dig in so that you can master this important algebra concept!

What is a Linear Inequality?

A linear inequality is a type of statement in algebra that compares two linear equations. To make this comparison, we place an inequality symbol in between the two sides of the inequality. For example, \(x+1>2x-1\).

Take a moment to review this inequality symbol list:

  • < (less than)
  • > (greater than)
  • ≤ (less than or equal to)
  • ≥ (greater than or equal to)

Linear inequalities are similar to linear equations, however instead of an equals sign, a linear inequality contains one of the inequality symbols from the above list.

How to Solve a Linear Inequality

The steps that you take to solve a linear inequality are a very similar to those that you would take while  solving an algebraic equation . When solving linear inequalities, you often perform similar operations as you would when  solving linear equations . 

Just like in linear equations, you can add or subtract terms on both sides, and multiply or divide by constants on both sides. However, unlike solving linear equations, linear inequalities have one  very  important rule:

Remember: If you multiply or divide both sides of an inequality by a negative number, the inequality sign must be flipped! 

You will see some examples of this in the solving linear inequalities worksheets linked below!

Another important difference between solving a linear equation and solving a linear inequality is that the solution to a linear inequality will be the  set of all values  that make the inequality true (rather than just a  single value  that makes the equation true).

The solution to a linear inequality will tell you the places on the graph where one line is greater than or less than the other.

For example, consider the coordinate plane below that shows two lines in slope-intercept form. 

the graph of x+1 shown in red, the graph of 2x-1 shown in green

As you can see, the red line is above the green line as long as \(x<2\). After this, the green line is above the red line. So if we wanted to write the solution to \(x+1>2x-1\), we would say that the solution set is \(x<2\), or all x-values less than 2 (note that we do not include 2 in the solution set since that is the point where the lines are equal ).

Solving Algebraically

In order to solve \(x+1>2x-1\) algebraically, we will use the same algebra strategies that we use when solving linear equations. We will collect all x-terms on the left side of the equation, and all non-variable terms on the right side of the equation.

\begin{split} x+1&>2x-1 \\ \\ -x&>-2 \\ \\ x&<2 \end{split}

Since we had to divide both sides by -1, notice that we flipped the sign of the inequality symbol! Therefore, the solution to this inequality is x<2 (which we can confirm using the coordinate plane above).

Another way that we can represent this solution is on a number line . We draw a line to the left of 2 with a hollow circle at 2 to indicate that 2 is  not  part of our solution set. We would use a filled in dot to indicate a value that  is  part of the solution set.

the solution to two different linear inequalities represented on a number line

There are many ways to solve linear inequalities and represent their solutions. In the math worksheets that follow below, you will focus mainly on solving algebraically and representing your answer on a number line!

One-Step Inequalities Math Worksheet

To get started, try the set of one-step inequalities in the worksheet linked below. These problems will help you become familiar with solving a linear equality algebraically, and representing the solution on a number line. 

I have created this worksheet in PDF format for your convenience. Remember to check the answer key provided to make sure that you understand the basics of solving linear inequalities.

Download the PDF worksheet by clicking below!

Multi-Step Inequalities Math Worksheet

Now that you have had some practice with solving one-step inequality problems, use the following worksheet to try your hand at some more complex linear inequality problems. This worksheet contains two-step inequalities as well as some more difficult multi-step linear inequality problems! 

This worksheet is also provided in PDF format for ease of access. Remember to check the answer key to confirm your understanding of solving more complex linear inequalities.

Practice Solving Linear Inequalities

Inequalities may seem scary at first because of the inequality symbol, but as you have seen, they are actually solved in a very similar way to linear equations.

Use the math worksheets linked above to practice getting comfortable with solving a variety of linear inequality problems. Like any math concept, the more you practice the more familiar the concept will start to feel.

I hope these solving linear inequalities worksheets have helped you practice your inequality solving skills, as well as representing the solution set on a number line!

Ready to start applying your skills? Check out this linear inequalities word problems worksheet !

Did you find these solving linear inequalities worksheets helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Writing Inequalities from Word Problems

Learn about writing inequalities from word problems with help from our practice examples. If you want to test yourself, or get some practice, then try one of our graded worksheets, or our online quiz.

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What is an Inequality?

The language of inequalities.

  • How to Write an Inequality from a Word Problem
  • Write an Inequality from a Word Problems Examples

Writing Inequalities from Word Problems Worksheets

  • Writing Inequalities from Word Problems Online Quiz
  • More related resources

An inequality is when you have a relationship between two values of expressions which are not equal to each other.

There are a few different options for different types of inequalities:

  • Greater than (>) where one expression or value is greater than another, e.g. 7 > 5
  • Less than (<) where one expression or value is less than another, e.g. 9 < 2 x 6
  • Greater than or equal to (≥) where one expression or value is greater than or equal to another, e.g. 20 + 4 ≥ 17
  • Less than or equal to (≤) where one expression or value is less than or equal to another, e.g. 18 ≤ 9 x 2
  • Not equal to (≠) where one expression or value is not equal to another, e.g. 7 ≠ 4

When writing inequalities from word problems, we have to look carefully at and understand the language being used.

Different words and phrases have different meanings when deciding on which inequality to use.

The mathematical notation is really just a shorthand way of writing the words more efficiently and clearly.

Here is a quick table showing some of the written expressions often used and which inequality they are represented by.

Note: the word 'between' is mainly used to mean between inclusively (including end points).

However, sometimes 'between' is used to mean between exclusively (excluding end points).

To avoid ambiguity, it is good practice to include the word 'inclusive' or 'exclusive' to make it completely clear if the end points are included or not.

Some simple examples showing inequalities from phrases:

The variable names (letters) have been chosen at random - you can use any variable name to represent any value.

Note: you need to read the word problem carefully because sometimes the inequality does not match the language used, especially when the inequality involves finding out what is left over or what remains after an amount is taken away. See Examples 2) and 7) below.

How to Write Inequalities from Word Problems

When we are writing an inequality from a word problem, we are basically translating the word problem into mathematical language and symbols.

When writing an inequality from a word problem, there are two simple steps you need to follow...

Step 1) Read the word problem carefully and change the word problem into algebra.

  • use the language of inequalities table to help you select the right inequality

Step 2) Use algebra to solve the word problem

Step 3) rewrite the inequality using algebra., write an inequality from a word problem examples.

The best way to learn how to write inequalities from word problems and see how they work is to look at some ready made examples.

Writing Inequalities from Word Problems - Basic Examples

Here are some examples of writing inequalities from word problems.

Example 1) Sally bakes some cookies and needs to put them in the over for at least 12 minutes. Write an inequality using the variable t to show how long the cookies need to be baked in the oven.

The vocabulary which tells us about the inequality are the words: at least .

This means we need to use the ≥ symbol.

So the inequality is t ≥ 12 minutes

Example 2) Newton has a 30 ounce bottle of water. He drinks over half of the bottle. Write an inequality using the variable c to show how many ounces are left in the bottle.

The vocabulary which tells us about the inequality are the words: over .

However, because he has drunk over half the bottle, it means that there is under half a bottle left.

So the symbol we need is < and the amount is ½ of 30 = 15.

So the inequality is b < 15 ounces

Example 3) Anna is more than three times as old as Bertie. If Bertie is 8 years old, write an inequality using the variable A to show how old Anna is.

The vocabulary which tells us about the inequality are the words: more than .

So the symbol we need is > and the amount is 3 x 8 = 24.

So the inequality is A > 24 years old

Example 4) A book has 14 chapters.The shortest chapter has 12 pages. Write an inequality using the variable p to show how many pages the book has.

The vocabulary which tells us about the inequality are the words: shortest .

If the shortest chapter has 11 pages, then there must be some chapters with more than 11 pages.

So the symbol we need is > and the amount is 14 x 12 = 168.

So the inequality is p > 168 pages.

Writing Inequalities from Word Problems -Intermediate Examples

These examples use two different variables and express one variable in terms of another.

Example 5) Captain and Frazer have some gold coins. Captain has at least three times as many coins as Frazer. Write an inequality for the number of coins Captain has (c) in terms of the number of coins Frazer has (f).

So the symbol we need is ≥

So the inequality is c ≥ 3f.

Example 6) In a hotel there are f flights of stairs. Each flight has a maximum of 12 steps. There are also 3 steps up to the main entrance. Write an expression for the total number of steps, s, in terms of f.

The vocabulary which tells us about the inequality are the words: a maximum of .

So the symbol we need is ≤

We know that there are f flights of steps and also 3 extra steps.

So the inequality is s ≤ 12f + 3.

Writing Inequalities from Word Problems - Harder Examples

These examples involve solving word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

There are also examples where the variable lies between two values.

Example 7) Captain has a one-liter bottle of water. He drinks more than one-quarter of the bottle but less than one-half of the bottle. Write an inequality using the variable b to show the amount of water than is left in the bottle.

The vocabulary which tells us about the inequality are the words: more than and less than .

However, because we are looking at what is left in the bottle, rather than what has been drunk, we need to think carefully about the inequalities!

He drinks more than one-quarter of the bottle, so there will be less than three-quarters of the bottle left, so we need the symbol <

He drinks less than one-half of the bottle, so there will be one-half or more of the bottle left, so we need the symbol ≥

Half of the bottle = ½ liters = 500 ml. 1000 - 500 = 500 ml

Quarter of the bottle = ¼ liters = 250 ml. 1000 - 250 = 750 ml

So the inequality is b ≥ 500 ml and b < 750 ml This can be simplified to: 500 ≤ b < 750 ml This means that he has at least 500 ml but less than 750 ml left.

Example 8) Captain has challenged himself to catch a minimum of 50 fish from a lake. He manages to catch 8 of them and put them in his bucket. If he catches 6 fish every hour, write an inequality to show the time (t) in hours it will take him to reach his target.

The vocabulary which tells us about the inequality are the words: a minimum of .

The inequality we get from this problem is 6t + 8 ≥ 50

We are not finished yet, because this needs to be simplified and written in terms of t.

6t + 8 ≥ 50 so 6t ≥ 42

If we divide both sides of this inequality by 6, we get:

So the inequality is t ≥ 7 hours He needs to fish for at least 7 hours to reach his target.

Example 9) It takes Newton between 23 and 28 seconds (inclusive) to swim a length of a swimming pool. Write an inequality using the variable t to show how long it will take him to swim 3 lengths.

The vocabulary which tells us about the inequality are the words: between (inclusive) .

So the symbol we need is ≤ and ≥

3 x 23 = 69 and 3 x 28 = 84

So the inequality is t ≥ 69 and t ≤ 84 This can be simplified to: 69 ≤ t ≤ 84 It will take him between 69 and 84 seconds (inclusive) to swim 3 lengths.

We have a range of different inequality worksheets which involve writing inequalities from a range of word problems..

We have split the sheets into 3 sections: A, B and C

  • Section A involves basic level questions aimed at 6th grade
  • Section B involves medium level questions aimed at 6th and 7th grade
  • Section C involves more advanced questions aimed at 7th and 8th grade

Writing Inequalities from Word Problems - Section A Easier

Sheet 1 involves picking the vocabulary and relevant information from the problem and writing the inequality

Sheet 2 involves the same skills as Sheet 1, but also involves an arithmetic operation to get the inequality.

  • Inequalities from Word Problems Sheet A1
  • PDF version
  • Inequalities from Word Problems Sheet A2

Writing Inequalities from Word Problems - Section B Medium

Sheet 1 involves using two variables and writing an inequality for one variable in terms of the other variable

Sheet 2 is similar to Sheet 1 but with slightly harder problems.

  • Inequalities from Word Problems Sheet B1
  • Inequalities from Word Problems Sheet B2

Writing Inequalities from Word Problems - Section C

Sheet 1 involves using one variables and using the information to solve the inequality, usually in the form px + q > r or px + q < r, where p, q, and r are specific rational numbers

Sheet 2 involves the same skills as Sheet 1 but has compound inequalities in each question

  • Inequalities from Word Problems Sheet C1
  • Inequalities from Word Problems Sheet C2

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Inequalities on a Number Line Worksheets

  • Inequalities on a Number Line

6th Grade Ratio and Unit Rate Worksheets

These 5th grade ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

  • Ratio Part to Part Worksheets
  • Ratio and Proportion Worksheets
  • The Definition of Unit Rate
  • Unit Rate Problems 6th Grade

6th Grade Algebra Worksheets

If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

  • Generate the algebra - and write your own algebraic expressions;
  • Calculate the algebra - work out the value of different expressions;
  • Solve the algebra - find the value of the term in the equation.
  • Use the distributive property to factorize and expand different expressions
  • 6th Grade Distributive Property Worksheets
  • Expressions and Equations 6th Grade
  • Basic Algebra Worksheets (6th & 7th Grade)

Writing Inequalities from Word Problems Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

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We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your skill at writing inequalities from a range of word problems.

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Inequalities Word Problems Worksheet

Related resources.

The various resources listed below are aligned to the same standard, (7EE04) taken from the CCSM ( Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

  • Solve word problems leading to equations of the form  px  +  q  =  r  and  p ( x  +  q ) =  r , where  p ,  q , and  r  are specific rational numbers . Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.  For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
  • Solve word problems leading to inequalities of the form  px  +  q  >  r  or  px  +  q  <  r , where  p ,  q , and  r  are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.  For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Example/Guidance

  • Solving Simple Equations in 2 Steps

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

  • Equations with subtraction  e.g. x – 4 = 2 (From Worksheet)
  • Equations with division  e.g. n/2 = 12 (From Worksheet)
  • Subtraction & addition equations (1 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
  • Subtraction & addition equations (2 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
  • Multiplication & division equations (1 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
  • Multiplication & division equations (2 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
  • Addition, subtraction, multiplication & division equations  (From Worksheet)
  • Solving equations in two steps (1 of 4)  e.g. 5n + 4 = 29 (From Worksheet)
  • Solving equations in two steps (2 of 4)  e.g. a/4 + 3 = 7 (From Worksheet)
  • Solving equations in two steps (3 of 4)  e.g. 7n – 3 = 18 (From Worksheet)
  • Solving equations in two steps (4 of 4)  e.g. b/9 – 4 = 6 (From Worksheet)

Linear Inequalities Worksheets

Worksheets on linear inequalities will help students practice different questions on inequalities. Linear inequalities worksheets help students recall this topic to solve linear inequation, find the solution and represent the solution set of an inequation on a real line.

Benefits of Linear Inequalities Worksheets

Each graphing linear inequalities worksheet on this page has four coordinate planes and linear inequalities in slope-intercept form and includes an answer key showing the correct graph.

Printable PDFs for Linear Inequalities Worksheets

These worksheets help students to know more deeply about linear inequalities and their functions. These math worksheets are a helpful guide for kids as well as their parents to see and review their answer sheets. Students can download the PDF format of these easily accessible linear inequalities worksheets to practice and solve questions for free.

IMAGES

  1. Inequalities Worksheets with Answer Key

    problem solving inequalities worksheet

  2. Solving One Step Inequalities Worksheet

    problem solving inequalities worksheet

  3. Solving Two Step Inequalities Worksheet

    problem solving inequalities worksheet

  4. Solving Inequalities Worksheet for 7th

    problem solving inequalities worksheet

  5. Solving Inequalities Worksheet for 6th

    problem solving inequalities worksheet

  6. Worksheet: Solving Linear Inequalities by No-Frills Math Practice

    problem solving inequalities worksheet

VIDEO

  1. Solving Inequalities and graphing the solution set

  2. Solving Inequalities by Subtraction in 2 minutes

  3. Solving Inequalities and graphing the solution set

  4. Solving Inequalities Word Problem EX2

  5. Solving Quadratic Inequalities

  6. Solving Inequalities and graphing the solution set

COMMENTS

  1. Inequalities Worksheets

    View Answers Solving Inequalities Worksheet 3 - Here is a twelve problem worksheet featuring two-step inequalities. Use inverse operations or mental math to solve for x. Solving Inequalities Worksheet 3 RTF Solving Inequalities Worksheet 3 PDF Preview Solving Inequalities Worksheet 3 in Your Browser View Answers

  2. Inequalities Worksheets

    Solutions to inequalities are infinite and are presented as an interval. Kick-start practice with our free inequalities worksheets! Exclusive Inequalities Worksheets » Translating Inequality Phrases » Compound Inequalities » One Step Inequalities » Graphing Linear Inequalities » Two Step Inequalities » Absolute Value Inequalities

  3. Pre-Algebra Worksheets

    One Step Multiply & Divide Inequalities Worksheets Two Step Inequalities Inequalities Worksheets Multiple Step Inequalities Inequalities Worksheets Detailed Description for All Inequalities Worksheets Properties of Inequality Handout This Inequality Worksheet will create a handout for the properties of inequalities.

  4. Inequalities Word Problem Worksheet

    Answers to Inequalities Word Problem Worksheet 1) No more than 12 weeks 4) At least 12 more sessions 6) More than 12.5 weeks. 8) No solution. : 10 12 14 16 10) x £ -1 : 18

  5. PDF Solving Inequalities

    (a) Question 9: Find the integers that satisfy each of the inequalities below (a) (c) Apply O Question 1: Lauren goes shopping and has £50 to spend. She bought a T-shirt and 3 pairs of leggings. The T-shirt cost £23. Each pair of leggings cost £x Form an inequality in terms of x. Solve the inequality to Jind the possible price of the leggings.

  6. How to Solve Inequalities—Step-by-Step Examples and Tutorial

    3x/3 < 18/3. x < 6. Solving this example required two steps (step one: subtract 8 from both sides; step two: divide both sides by 3). The result is the solved inequality x<6. The step-by-step procedure to solving example #2 is illustrated in Figure 04 below. Figure 04: How to solve an inequality: 3x+8<26.

  7. PDF Solving Inequalities Date Period

    22) Name one particular solution to question #20. 22) Name one particular solution to question #20. Any number greater than zero. Ex: 4.7. Many answers. Ex: 2 x ≥ x + 2. Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com.

  8. Inequalities Worksheets

    Solve and graph the inequalities with only one variable. Students graph the inequality. They do not need to perform any steps to isolate the variable. (example: a ≥ 7) One-Step Inequalities. These inequality worksheets have one variable in each problem. Students need to isolate the variable using only one step. (example: 12 - x ≤ 8)

  9. The Best Teacher-Approved Solving Inequalities Worksheets

    The Solving 1 and 2-Step Inequalities worksheet is intended to teach grade 7 students number system standards. The sheets are to be used by pupils who already know how to solve 1- and 2-step linear equations. Note that the sheets do not have instructions on solution steps, except for division by negative numbers.

  10. PDF Multi-Step Inequalities Date Period

    Solve each inequality and graph its solution. 1) ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Multi-Step Inequalities.ks-ia1 Author: Mike Created Date: 9/11/2012 2:38:45 PM ...

  11. Solving Inequalities Textbook Exercise

    The Textbook Exercise on Solving Inequalities. ... Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. ... inequality. Textbook Exercise. Previous: Inequalities Textbook Exercise. Next: Graphical Inequalities 1 Textbook Exercise. GCSE Revision Cards. 5-a-day Workbooks. Primary Study Cards ...

  12. Inequalities Worksheets with Answer Key

    The worksheets given here require students to solve inequalities in the regular way and also on the number line. Some of the questions ask you to find the inequality variables' values. More Radicals Worksheets Compound Inequalities Worksheets Graphing Inequalities Worksheets Inequality Word Problems Worksheets Systems of Inequalities Worksheets Solving Equations and Inequalities Worksheets ...

  13. Solving Inequalities

    Here are the details: Adding or Subtracting a Value We can often solve inequalities by adding (or subtracting) a number from both sides (just as in Introduction to Algebra ), like this: Example: x + 3 < 7 If we subtract 3 from both sides, we get:

  14. Inequalities Word Problems Worksheets

    Inequalities word problems worksheets gives students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. Inequalities word problems worksheets helps kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of inequalities.

  15. Inequalities Practice Questions

    . Click here for Answers inequality Practice Questions Previous: Graphical Inequalities Practice Questions Next: Cumulative Frequency and Box Plot Practice Questions The Corbettmaths Practice Questions on inequalities

  16. Solving Inequalities Worksheets Teaching Resources

    TWO worksheets are included in this set: 1) Solving and graphing one step inequalities (addition and subtraction) 2) Solving and graphing one step inequalities (multiplication and division) Problems inc Subjects: Algebra, Math Grades: 7th - 8th Types: Activities, Worksheets CCSS: 7.EE.B.4a

  17. PDF Solving One-Step Inequalities by Adding/Subtracting Date Period

    R o 3AwlvlR 1r Si Ogdh WtasW Crge Ns1evruvce nd w.6 X 5M ma cdhe M 6w Ei Jt jh a eIWn7f3iQn ZiGt ne7 tP Fr1eZ-GATlmgIedbtr 0ai. 8 Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Solving One-Step Inequalities by Adding/Subtracting Date_____ Period____

  18. Solving Inequality Word Questions

    Solving Inequality Word Questions (You might like to read Introduction to Inequalities and Solving Inequalities first.) In Algebra we have "inequality" questions like: Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals.

  19. Algebra 2 Worksheets

    These Equations and Inequalities Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

  20. Solving Linear Inequalities Worksheets with Solutions

    A linear inequality is a type of statement in algebra that compares two linear equations. To make this comparison, we place an inequality symbol in between the two sides of the inequality. For example, x + 1 > 2x − 1. Linear inequalities are similar to linear equations, however instead of an equals sign, a linear inequality contains one of ...

  21. Writing Inequalities from Word Problems

    Step 1) Read the word problem carefully and change the word problem into algebra. use the language of inequalities table to help you select the right inequality Step 2) Use algebra to solve the word problem Step 3) Rewrite the inequality using algebra.

  22. Inequalities Word Problems Worksheet

    Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p , q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100.

  23. Linear Inequalities Worksheets

    Linear inequalities worksheets help students recall this topic to solve linear inequation, find the solution and represent the solution set of an inequation on a real line. Benefits of Linear Inequalities Worksheets