Wayground
Solving One Step Inequality - Printable Mathematics Worksheets - Wayground

Solving One Step Inequality

9 questions

9th - 12th Grade

Mathematics

Solving One Step Inequality is a free printable mathematics worksheet for students in Grades 9–12. It includes 16 questions, primarily multiple-choice items, that focus on solving one-step inequalities by isolating a variable with the correct inverse operation. Students identify whether to add, subtract, multiply, or divide, then select solutions such as y ≥ 5 for y + 7 ≥ 12 and x < 6 for 8x < 48. The worksheet also emphasizes the key rule for multiplying or dividing by a negative number: reverse the inequality symbol to preserve the correct relationship between both sides. Questions ask students to apply this rule, recognize why the sign changes, and solve inequalities involving positive and negative coefficients or constants. This format provides focused practice and a quick way to check conceptual understanding. The worksheet is available as a free printable PDF with a complete answer key and is suitable for guided practice, independent work, or review.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Solving One Step Inequality

Total questions: 9

Name
Class
Date
1.
a)

x > -4

b)

x < -4

c)

x < -4

d)

x > -4

2.
y + 7 ≥ 12
a)
y ≥ 5
b)
y ≤ 5 
c)
y ≥ 19 
d)
y ≤ 19
3.
Solve
8x < 48
a)
x < -6
b)
x > -6
c)
x < 6
d)
x > 6
4.

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

5.

What is the solution to the following inequality? 3m−2>73m-2>7  

a)

m > 3

b)

m < 3

c)

m = 3

d)

m > 5/3

6-12.

Answer the questions below after watching the video

6.

What operation is used to isolate y in the inequality y + 7 < 8?

a)

Multiplication

b)

Division

c)

Addition

d)

Subtraction

7.

In the inequality x/5 ≥ 3, what operation is used to isolate x?

a)

Division

b)

Subtraction

c)

Addition

d)

Multiplication

8.

What is the solution to the inequality x/5 ≥ 3 after isolating x?

a)

x ≤ 15

b)

x ≥ 15

c)

x < 15

d)

x > 15

9.

In the inequality 14 ≥ n - 11, what operation is used to isolate n?

a)

Subtraction

b)

Multiplication

c)

Addition

d)

Division

10.

What is the correct solution for the inequality 14 ≥ n - 11 after isolating n?

a)

n > 25

b)

n ≥ 25

c)

n < 25

d)

n ≤ 25

11.

Why do we flip the inequality sign when dividing by a negative number?

a)

To correct the direction of the inequality

b)

To balance both sides of the inequality

c)

To make the inequality false

d)

To simplify the inequality

12.

What is the solution to the inequality -6r < 36 after isolating r and flipping the sign?

a)

r > -6

b)

r < -6

c)

r ≥ -6

d)

r ≤ -6

13.
Solve 
a)
a≤1
b)
a≤25
c)
a>1
d)
a<25
14.
Solve 
-9h > (-63)
a)
h < 7
b)
h > 7
c)
h < -7
d)
h > -7
15.
Solve
a)
x < -96
b)
x < 20
c)
x = 6
d)
x > 96
Answer Key

Solving One Step Inequality

Total questions: 9

1.
a)

x > -4

2.
a) y ≥ 5
3.
c) x < 6
4.
a)

when multiplying or dividing by a NEGATIVE

5.
a)

m > 3

6-12.
6.
d)

Subtraction

7.
d)

Multiplication

8.
b)

x ≥ 15

9.
c)

Addition

10.
d)

n ≤ 25

11.
a)

To correct the direction of the inequality

12.
a)

r > -6

13.
b) a≤25
14.
a) h < 7
15.
a) x < -96

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this one-step inequalities worksheet help students learn?

This Grade 9–12 mathematics worksheet helps students solve one-step inequalities by choosing the inverse operation needed to isolate a variable. Its 15 multiple-choice questions and one additional comprehension-video item address addition, subtraction, multiplication, and division, including when and why to reverse the inequality symbol after multiplying or dividing by a negative number.

How can I use this worksheet to teach solving one-step inequalities?

First model how an inverse operation isolates the variable, using a simple inequality such as y + 7 ≥ 12. Then have students explain which operation they would use for items such as x/5 ≥ 3 or 14 ≥ n − 11 before solving them. Pause before the negative-coefficient questions to ask why multiplying or dividing by a negative reverses the inequality symbol, and use the multiple-choice options to discuss incorrect reasoning.

What mistakes should I watch for when students solve these one-step inequalities?

Watch for students choosing the wrong inverse operation, such as adding instead of subtracting to isolate a variable in y + 7 ≥ 12, or dividing when multiplication is needed for x/5 ≥ 3. Students may also reverse the inequality for any negative-looking expression rather than specifically when multiplying or dividing by a negative number. Check that they apply the sign change in negative-coefficient problems and select the resulting inequality direction, not just the numerical boundary.

How do I assign and grade this one-step inequalities worksheet?

You can assign Solving One Step Inequality as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also supports classrooms that are reducing screen time.

How can I differentiate this one-step inequalities worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the inequality symbols, variables, and multiple-choice options are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language. These changes preserve the one-step inequality practice while making the worksheet format more accessible.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion