Wayground
Solving two step equations and inequalities - Printable Math Worksheets class 8 - Wayground

Solving two step equations and inequalities

James Mcclellan

Created by James Mcclellan

12 questions

8th Grade

Math

Updated Sept 2026

This Grade 8 mathematics worksheet gives students focused practice solving two-step equations and inequalities. Across 12 items, students identify the correct first and last steps for solving equations, translate verbal statements such as “no more than” and “more than” into inequalities, and solve inequality expressions. The worksheet also includes a drag-and-drop item on open and closed circles, a matching activity connecting inequalities to number-line graphs, and multi-step word problems involving budgets and unit costs. As a free printable worksheet with an answer key, it supports guided instruction, independent practice, review, or a quick assessment of algebraic reasoning. Students must connect symbolic manipulation with inequality notation, graphing conventions, and real-world situations. The varied question formats help teachers see whether students can perform the algebraic steps, interpret inequality language, and select a graph or model that represents a solution.

Worksheet settings

Font size

S
M
L
XL
WaygroundWorksheets

Solving two step equations and inequalities

Total questions: 12

Name
Class
Date
1.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
2.

Solve the inequality 18<x4−218<\frac{x}{4}-2  

a)

80<x80<x  

b)

5<x5<x  

c)

4<x4<x  

d)

64<x64<x  

3.
Question Image
a)

b)

c)

d)

4.
Translate the following phrase: Tom can spend no more than 20 dollars on his mom's birthday present.
a)
t > 20
b)
t < 20
c)
t ≤ 20
d)
t ≥ 20
5.
Translate the following phrase: You and your friends ate more than 8 slices of pizza at the party.
a)
x > 8
b)
x < 8
c)
x ≤ 8
d)
x ≥ 8
6.

When graphing inequalities:

Use an open circle for ​​ (a)   .

Use a closed circle for ​​​​ (b)   .

Choose from the below words
> or <
≥ or ≤
7.

Match each statement with the correct graph.

Match each statement with the correct graph.

y < 6

Match each statement with the correct graph.

y > 6

Match each statement with the correct graph.

y ≤ 6

Match each statement with the correct graph.

y ≥ 6

8.

What would be the first step in solving the equation for 2x+7=15?

a)

Add 7 to both sides

b)

Subtract 7 from both sides

c)

Divide both sides by 2

d)

Multiply both sides by 2

9.

What would be the last step in solving the equation X6−2=12\frac{X}{6}-2=12  ?

a)

Add 2 to both sides

b)

Subtract 2 from both sides

c)

Multiply both sides by 6

d)

Divide both sides by 6

10.

The solution to the inequality 5x − 4 > 21 is represented by which number line?

a)
The solution to the inequality 5 x − 4 > 21 is represented by which number line?
b)
The solution to the inequality 5 x − 4 > 21 is represented by which number line?
c)
The solution to the inequality 5 x − 4 > 21 is represented by which number line?
d)
The solution to the inequality 5 x − 4 > 21 is represented by which number line?
11.

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $19.00 to buy the scrapbook. Each sheet of paper costs $3.00. How many sheets of paper can she buy?

a)

12

b)

7

c)

-7

d)

8

12.
Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?
a)
10x + 1.50 ≥ 40
b)
1.50x + 10 ≤ 40
c)
1.50x + 10 <40
d)
10x + 1.50 < 40
WaygroundAnswer Key

Solving two step equations and inequalities

Total questions: 12

1.
a) x ≥ - 10
2.
a)

80<x80<x  

3.
d)
4.
c) t ≤ 20
5.
a) x > 8
6.
> or <, ≥ or ≤
7.
 - 

y < 6

,  - 

y > 6

,  - 

y ≤ 6

,  - 

y ≥ 6

8.
b)

Subtract 7 from both sides

9.
c)

Multiply both sides by 6

10.
b)
11.
b)

7

12.
b) 1.50x + 10 ≤ 40

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this worksheet cover?

This Grade 8 worksheet covers solving two-step equations and inequalities, translating phrases such as “no more than” and “more than” into inequality symbols, and representing solutions on number lines. Its 12 items use multiple choice, drag-and-drop, and matching formats to check algebraic steps, open versus closed circles, graph selection, and budget-based word problems.

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

Begin by modeling how to undo operations in reverse order, then have students identify the first or last step in the worksheet’s equation-solving items. Next, connect phrases such as “no more than” and “more than” to inequality symbols before students use open or closed circles and match statements to number-line graphs. Finish with the scrapbook and fair-budget problems so students translate a situation into an inequality and interpret the result.

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

Watch for students choosing the wrong inequality symbol for phrases such as “no more than” and “more than,” or reversing the inequality when a negative operation is involved. Students may also use an open circle for a less-than-or-equal-to or greater-than-or-equal-to endpoint, select the wrong first or final inverse operation, or confuse the fixed admission cost with the per-ride or per-sheet cost in the word problems.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade digital responses in Wayground or scan students’ printable work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the algebraic expressions, answer choices, and number-line matching items are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate for students working through the inequality language and word problems.

Where can I find more worksheets like this on Wayground?

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

© 2026 Wayground Inc.

Accessibility and Inclusion