ABSOLUTE VALUE OF INTEGERS WORKSHEET

Problem 1 :

Find the absolute value of the integer -9. 

Problem 2 : 

Find the absolute value of the integer 9. 

Problem 3 : 

Find the absolute value of (-17 + 8). 

Problem 4 : 

Find the absolute value of (28 - 13).

Problem 5 : 

If |x| is an integer between 0 and 3, then, find all possible values of x.  

Problem 6 :

If |2x - 1| is an integer between 3 and 6, then, find all possible values of x.  

Problem 7 :

Solve for x : 

|3x + 5|  =  7

Problem 8 :

Solve for x : 

|7x|  =  21

Problem 9 :

Solve for x :

2|3x +4|  =  8

Problem 10 :

Solve for x : 

3|5x - 6| - 4  =  5

Detailed Answer Key

Problem 1 :

Find the absolute value of the integer -9. 

Solution : 

|-9|  =  9

Problem 2 : 

Find the absolute value of the integer 9. 

Solution : 

|9|  =  9

Problem 3 : 

Find the absolute value of (-17 + 8). 

Solution : 

|-17 + 8|  =  |-9|

|-17 + 8|  =  9

Problem 4 : 

Find the absolute value of (28 - 13). 

Solution : 

|28 - 13|  =  |15|

|28 - 13|  =  15

Problem 5 : 

If |x| is an integer between 0 and 3, then, find all possible values of x.  

Solution : 

Given : |x| is an integer between 0 and 3. 

Then, we have

|x|  =  1  and  |x|  =  2

Solve for x in |x|  =  1. 

Solve for x in |x|  =  2. 

So, the possible values of x are 

-2, -1, 1, 2

Problem 6 :

If |2x - 1| is an integer between 3 and 6, then, find all possible values of x.  

Solution : 

Given : |2x - 1| is an integer between 3 and 6. 

Then, we have

|2x - 1|  =  4  and  |2x - 1|  =  5

Solve for x in |2x - 1|  =  4. 

Solve for x in |2x - 1|  =  5. 

So, the possible values of x are 

-2, -3/2, 5/2, 3

Problem 7 :

Solve for x : 

|3x + 5|  =  7

Solution :

|3x + 5|  =  7

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-4, 2/3

Problem 8 :

Solve for x : 

|7x|  =  21

Solution :

|7x|  =  21

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-3, 3 

Problem 9 :

Solve for x :

2|3x +4|  =  8

Solution :

2|3x +4|  =  7

Divide each side by 2. 

|3x + 4|  =  4

The expression inside the absolute value can be either positive or negative. 

Then, we have

So, the values of x are 

-8/3, 0

Problem 10 :

Solve for x : 

3|5x - 6| - 4  =  5

Solution :

3|5x - 6| - 4  =  5

Add 4 to each side.

3|5x - 6|  =  9

Divide each side by 3.

|5x - 6|  =  3

So, the values of x are 

3/5, 9/5

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