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absolute value equations - Printable Mathematics Worksheets grade 9 - Wayground

absolute value equations

16 questions

9th - 9th Grade

Mathematics

This Grade 9 mathematics worksheet develops students’ ability to solve absolute value equations and explain the reasoning behind each solution. Across 16 items, students identify absolute value as distance from zero, isolate an absolute value expression before solving, recognize when equations have two solutions or no solution, and determine values that satisfy equations such as |x| = 5, |2x| = 4, and |x − 3| = 2. The worksheet includes 10 multiple-choice questions, 3 multiple-select questions, 2 open-ended prompts about solution steps, and 1 matching item. Use this free printable worksheet to check both procedural fluency and conceptual understanding. Multiple-select questions require students to select both valid values, while open-ended items reveal whether they can explain the solving process rather than only identify an answer. The complete answer key supports efficient review, reteaching, or independent practice in a Grade 9 math lesson.

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absolute value equations

Total questions: 16

Name
Class
Date
1.

∣x∣= − 5\left|x\right|=\ -\ 5  

a)

5

b)

-5

c)

5 or -5

d)

no solution

2.

∣x∣ = 6\left|x\right|\ =\ 6  

a)

6

b)

-6

c)

6 or -6

d)

no solution

3.

What are the steps to solve this: 2 + ∣x−4∣ = 52\ +\ \left|x-4\right|\ =\ 5  

4 lines
4.

What are the steps to solve this: 3∣x+1∣ +2=43\left|x+1\right|\ +2=4  

4 lines
5.

∣x+5∣ = −3\left|x+5\right|\ =\ -3  

a)

−2 or −8-2\ or\ -8  

b)

no solution

c)

00  

6.

∣x+5∣=0\left|x+5\right|=0  

a)

no solution

b)

00  

c)

−5-5  

d)

−5 or 5-5\ or\ 5  

7.

Solve:
∣34a−3∣=9\left|\frac{3}{4}a-3\right|=9  

a)

{16, −8}\left\{16,\ -8\right\}  

b)

{16, −16}\left\{16,\ -16\right\}  

c)

{−8, 8}\left\{-8,\ 8\right\}  

d)

no solution

8.

What could the value of x be?

∣x∣=7|x|=7

Choose all that apply.

a)

7

b)

-7

c)

14

d)

0

9.

Solve for x

∣x+3∣=1|x+3|=1

Don't forget to choose two answers!

a)

-4

b)

4

c)

2

d)

-2

e)

I am not sure.

10.

Solve for x:

∣2x−3∣=5|2x-3|=5

Choose two answers.

a)

4

b)

-1

c)

1

d)

-4

e)

I am not sure.

11.

Match the following

|x| = 5

x = 5, -5

|2x| = 4

x = 2, -2

|x+2| = 6

x = 4, -8

|x-3| = 2

x = 1, 5

∣x5∣=−6\left|\frac{x}{5}\right|=-6  

No Solution

12.
What's a way to define absolute value?
a)
The value of a number
b)
The opposite of a number
c)
The distance of a number from zero
d)
The multiplicative inverse of a number
13.
What is the reason that absolute value is always written as a positive?
a)
Absolute value is talking about numbers so it must be positive.
b)
Absolute value does not always have to be positive.
c)
Absolute value is like a clock it has only positive numbers.
d)
Absolute value is talking about distance, distance is always measured by positive numbers.
14.
−2|−2r − 4| = -12
a)
{3,1}
b)
{-3,-1}
c)
{-3}
d)
No Solution
15.

What would be the correct way to write the problem before solving?

2|x-1|-6=4

a)

|x-1|=5

b)

x-1=5

c)

|x-1|=-5

d)

x-1=-5

16.

Solve for X

2|X+3|+3=1

a)

X= -4 and X= -2

b)

X=2 and X= -2

c)

X=0

d)

No Solution

Answer Key

absolute value equations

Total questions: 16

1.
d)

no solution

2.
c)

6 or -6

3.
n/a
4.
n/a
5.
b)

no solution

6.
c)

−5-5  

7.
a)

{16, −8}\left\{16,\ -8\right\}  

8.
a)

7

, b)

-7

9.
a)

-4

, d)

-2

10.
a)

4

, b)

-1

11.

|x| = 5

 - 

x = 5, -5

, 

|2x| = 4

 - 

x = 2, -2

, 

|x+2| = 6

 - 

x = 4, -8

, 

|x-3| = 2

 - 

x = 1, 5

, 

∣x5∣=−6\left|\frac{x}{5}\right|=-6  

 - 

No Solution

12.
c) The distance of a number from zero
13.
d) Absolute value is talking about distance, distance is always measured by positive numbers.
14.
b) {-3,-1}
15.
a)

|x-1|=5

16.
d)

No Solution

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FAQs

What does this absolute value equations worksheet cover?

This Grade 9 worksheet practices solving absolute value equations, including equations with two solutions and equations with no solution. Its 16 items combine multiple choice, multiple select, matching, and open-ended prompts, requiring students to isolate the absolute value expression, select all valid values, match related equations, and explain solution steps.

How can I use this worksheet to teach solving absolute value equations?

Begin by reviewing absolute value as distance from zero, then model how to isolate the absolute value expression before creating the positive and negative cases. Use the worksheet’s open-ended step prompts to have students explain their process, and follow with the multiple-select items so they must identify both solutions rather than stop after finding one. Discuss the no-solution examples to reinforce that an absolute value cannot equal a negative distance.

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

Watch for students choosing only one answer on the multiple-select equations, especially when both a positive and negative value satisfy the equation. Students may also begin solving before isolating the absolute value, treat absolute value as an opposite rather than a distance from zero, or miss that an isolated negative absolute value produces no solution. Check the open-ended responses for whether both cases and the required algebraic steps are shown.

How do I assign and grade this absolute value equations worksheet?

On Wayground, assign the worksheet as a printable PDF or as a digital quiz. It includes a complete answer key for the multiple-choice, multiple-select, matching, and open-ended items, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools working to reduce screen time.

How can I differentiate this absolute value equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation notation and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while students work through the absolute value equations, multiple-select choices, and open-ended solution steps.

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 support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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