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Solving and Graphing Two-Step Inequalities - Printable Mathematics Worksheets - Wayground

Solving and Graphing Two-Step Inequalities

10 questions

7th Grade

Mathematics

Solving and Graphing Two-Step Inequalities is a Grade 7 mathematics worksheet with 10 multiple-choice questions. Students solve inequalities by distributing, combining like terms, and isolating the variable; identify when to reverse the inequality symbol after multiplying or dividing by a negative; translate a situation into an inequality; and interpret or select number-line graphs. The items include symbolic problems, real-world inequality notation, graph interpretation, and open- or closed-dot conventions. This worksheet helps teachers check whether students can connect algebraic procedures with visual representations of inequality solutions. It is useful for guided practice, independent review, or a focused formative assessment after introducing two-step inequalities and graphing. The worksheet is available as a free printable PDF with a complete answer key, so teachers can quickly review students’ choices and identify whether errors come from solving, symbol selection, or graphing.

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Worksheets

Solving and Graphing Two-Step Inequalities

Total questions: 10

Name
Class
Date
1.

Let's kick it up another notch. Use what you know about distributing, combining like terms and solving two-step inequalities when solving for x.

7(x + 3) - 5x < 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

2.

Ok. Try this last one.Remember...use what you know about distributing, combining like terms and solving two-step inequalities when solving for x.


-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

3.

When do we switch the inequality symbol?

a)

when multiplying or dividing by a NEGATIVE

b)

when adding and subtracting a NEGATIVE

c)

we never switch the inequality

d)

When there is a negative in the problem

4.

Which inequality matches this situation? The maximum score on the pilot's test is 95 points.

a)

p < 95

b)

p > 95

c)

p ≥ 95

d)

p ≤ 95

5.

What inequality does the number line graph represent?

a)

x ≥ 3

b)

x > 3

c)

x < -3

d)

x ≤ -3

6.

Choose the correct graph that best describes the solution for each inequality.

a)

A

b)

B

c)

C

d)

D

7.

Which number line shows the solution to:
11x + 14 < –8? 

a)

a

b)

b

c)

c

d)

d

8.

Solve the inequality:  -3x + 4 > -2

a)

x < -1

b)

x > -1

c)

x < 2

d)

x > 2

9.

When graphing an inequality, you use an open dot when you use which symbols?

a)

<, >

b)

≤, ≥ 

10.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

Answer Key

Solving and Graphing Two-Step Inequalities

Total questions: 10

1.
c)

x<-4

2.
b)

x < 3

3.
a)

when multiplying or dividing by a NEGATIVE

4.
d)

p ≤ 95

5.
a)

x ≥ 3

6.
a)

A

7.
d)

d

8.
c)

x < 2

9.
a)

<, >

10.
d)

multiple or divide by a negative number

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FAQs

What does this worksheet cover?

This Grade 7 worksheet covers solving and graphing inequalities through 10 multiple-choice questions. Students practice distributing and combining like terms, isolating a variable, reversing the inequality when multiplying or dividing by a negative, translating a maximum-value situation, and matching inequalities with number-line graphs using open or closed dots.

How can I use this worksheet to teach solving and graphing two-step inequalities?

Use the symbolic inequality items to model distributing, combining like terms, and isolating the variable before moving to the graphing questions. Ask students to explain why the inequality symbol reverses in problems involving a negative factor and why strict inequalities use open dots while inclusive inequalities use closed dots. Finish by having students connect a solved inequality to its matching number-line representation.

What mistakes should I watch for when students complete this worksheet?

Watch for students who reverse the inequality symbol whenever a negative appears, rather than only when multiplying or dividing by a negative. Students may also confuse < or > with ≤ or ≥, choose the wrong open or closed dot, or select a graph whose direction does not match the solution. In the algebra items, check whether they distribute correctly and combine like terms before isolating x.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 10 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz. The printable format also gives schools an option for reducing screen time.

How can I differentiate this inequalities worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the algebraic expressions, answer choices, and number-line graph prompts easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate. These changes apply to the worksheet file students use for solving and graphing the inequalities.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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