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

Answers

1. Answer :

|-9|  =  9

2. Answer :

|9|  =  9

3. Answer :

|-17 + 8|  =  |-9|

|-17 + 8|  =  9

4. Answer :

|28 - 13|  =  |15|

|28 - 13|  =  15

5. Answer :

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

Then, we have

|x|  =  1  and  |x|  =  2

Solve for x in |x|  =  1. 

x  =  1

x  =  -1

Solve for x in |x|  =  2. 

x  =  2

x  =  -2

So, the possible values of x are 

-2, -1, 1, 2

6. Answer :

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. 

2x - 1  =  4

2x  =  5

x  =  5/2

2x - 1  =  -4

2x  =  -3

x  =  -3/2

Solve for x in |2x - 1|  =  5. 

2x - 1  =  5

2x  =  6

x  =  3

2x - 1  =  -5

2x  =  -4

x  =  -2

So, the possible values of x are 

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

7. Answer :

|3x + 5|  =  7

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

Then, we have

3x + 5  =  7

3x  =  2

x  =  2/3

3x + 5  =  -7

3x  =  -12

x  =  -4

So, the values of x are 

-4, 2/3

8. Answer :

|7x|  =  21

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

Then, we have

7x  =  21

x  =  3

7x  =  -21

x  =  -3

So, the values of x are 

-3, 3 

9. Answer :

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

3x + 4  =  4

3x  =  0

x  =  0

3x + 4  =  -4

3x  =  -8

x  =  -8/3

So, the values of x are 

-8/3, 0

10. Answer :

3|5x - 6| - 4  =  5

Add 4 to each side.

3|5x - 6|  =  9

Divide each side by 3.

|5x - 6|  =  3

5x - 6  =  3

5x  =  9

x  =  9/5

5x - 6  =  -3

5x  =  3

x  =  3/5

So, the values of x are 

3/5, 9/5

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