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Solving One & Two Step Inequalities - Printable Mathematics Worksheets - Wayground

Solving One & Two Step Inequalities

10 questions

9th - 9th Grade

Mathematics

This Grade 9 mathematics worksheet, “Solving One & Two Step Inequalities,” gives students 10 multiple-choice questions focused on solving and interpreting one- and two-step inequalities. Students select solutions for inequalities such as y + 7 ≥ 12, 8x < 48, and 3m − 2 > 7, while also identifying solution graphs, inequality symbols, and open-dot conventions. The worksheet reinforces essential reasoning steps: isolating the variable, recognizing when an inequality symbol must reverse after multiplying or dividing by a negative, and distinguishing strict inequalities from inclusive ones when reading or graphing solutions. It is useful for guided practice, independent review, or a quick Grade 9 mathematics check of conceptual understanding. This free printable worksheet includes a complete answer key for efficient checking and feedback.

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Solving One & Two Step Inequalities

Total questions: 10

Name
Class
Date
1.

Match the graph with its inequality.

a)

a > 11

b)

a < 11

c)

11 ≤ a

d)

11 ≥ a

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.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
7.
Pick the correct letter for:
6 > x
a)
A
b)
B
c)
C
d)
D
8.

Solve the inequality

a)

x<−6x<-6

b)

x≤−6x\le-6

c)

x≥−6x\ge-6

d)

x>−6x>-6

9.

Solve the inequality

a)

y<66y<66

b)

y>66y>66

c)

y>6y>6

d)

y<6y<6

10.

Solve the inequality

a)

 x>11x>11  

b)

 x>−11x>-11  

c)

 x<11x<11  

d)

 x<−11x<-11  

Answer Key

Solving One & Two Step Inequalities

Total questions: 10

1.
c)

11 ≤ a

2.
a) y ≥ 5
3.
c) x < 6
4.
a)

when multiplying or dividing by a NEGATIVE

5.
a)

m > 3

6.
a) <, >
7.
b) B
8.
c)

x≥−6x\ge-6

9.
a)

y<66y<66

10.
a)

 x>11x>11  

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FAQs

What does the Solving One & Two Step Inequalities worksheet cover?

This Grade 9 worksheet uses 10 multiple-choice questions to assess solving one- and two-step inequalities, interpreting inequality symbols, matching an inequality to its graph, and identifying open-dot conventions. Students practice isolating variables, selecting the correct solution set, and recognizing that multiplication or division by a negative reverses the inequality symbol.

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

Introduce the worksheet by modeling how to isolate a variable and then explicitly connect each algebraic step to the direction of the inequality. Before students work independently, discuss why multiplying or dividing by a negative reverses the symbol and why < and > use open dots. Use the multiple-choice options as discussion prompts by asking students to explain why a tempting alternative does not represent the correct solution.

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

Watch for students choosing a solution without reversing the inequality after multiplying or dividing by a negative, or treating any negative number in an expression as a reason to reverse the symbol. Students may also confuse open dots for < and > with the inclusive symbols ≤ and ≥, or select a boundary value without completing the isolation steps. The graph-matching and symbol-identification items can reveal whether the error is algebraic or related to graph notation.

How do I assign and grade this Solving One & Two Step Inequalities worksheet?

On Wayground, you can assign this worksheet as a printable PDF or as a digital quiz. 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 schools that want to reduce screen time while maintaining structured inequality practice.

How can I differentiate this inequalities worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the multiple-choice inequality expressions and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those changes will help students access the algebra and graphing vocabulary.

Where can I find more worksheets like this on Wayground?

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

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