# ABSOLUTE VALUE OF INTEGERS

The absolute value of an integer is the integer’s distance from 0 on a number line.

For example, the absolute value of -3 is 3.

To understand this, let us mark -3 on a number line.

On the above number line, -3 is 3 units from 0.

Since -3 is 3 units from 0, we say that the absolute value of "-3" is 3.

The absolute value of -3 is written |-3|.

And we have

|-3|  =  3

Because absolute value represents a distance and it is always positive.

## Solved Examples

Example 1 :

Find the absolute value of the integer -9.

Solution :

|-9|  =  9

Example 2 :

Find the absolute value of the integer 9.

Solution :

|9|  =  9

Example 3 :

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

Solution :

|-17 + 8|  =  |-9|

|-17 + 8|  =  9

Example 4 :

Find the absolute value of (28 - 13).

Solution :

|28 - 13|  =  |15|

|28 - 13|  =  15

Example 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

The possible values of x are

-2, -1, 1, 2

Example 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  =  42x  =  5x  =  5/2 2x - 1  =  -42x  =  -3x  =  -3/2

Solve for x in |2x - 1|  =  5.

 2x - 1  =  52x  =  6x  =  3 2x - 1  =  -52x  =  -4x  =  -2

So, the possible values of x are

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

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