**Absolute Value of Integers Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on finding absolute value of integers.

Before look at the worksheet, if you would like to learn the stuff fining absolute value of integers,

**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

**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.

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

**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.

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

**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

3x + 5 = 7 3x = 2 x = 2/3 |
3x + 5 = -7 3x = -12 x = -4 |

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

7x = 21 x = 3 |
7x = -21 x = -3 |

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

3x + 4 = 4 3x = 0 x = 0 |
3x + 4 = -4 3x = -8 x = -8/3 |

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

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

After having gone through the stuff given above, we hope that the students would have understood, how to find absolute value of integers.

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