Absolute value function is one of the topics in which we are going to see about solving for x in absolute value and graphing the absolute-value-function.

**Absolute value:**

The absolute value of a number is its distance from 0 on a number line. For example, the number "9" is 9 units away from zero. So its absolute value is 9. Negative numbers are more interesting compared to positive numbers,because the number -4 is still 4 units away from 0. The absolute value of the number -4 is therefore positive 4 .

**Examples of absolute value:**

- The absolute value of -9 is 9
- The absolute value of 5 is 5
- The absolute value of 0 is 0
- The absolute value of -256 is 256

**More examples of absolute value:**

| -5 + 8 | = 3

| -8 x 2 | = | -16 | = 16

| -13 + 5 | = | -8 | = 8

Example problem of solving x in absolute values

**| x + 9 | = 5 **__Solution:__

x + 9 = 5 (or) x + 9 = -5

x = 5 – 9 (or) x = -5 -9

x = -4 (or) x =-14

**The solution is -4 and -14 ****| x - 8 | = -9 **__Solution:__

x – 8 = -9 (or) x - 8 = 9

x = -9 + 8 (or) x = 9 + 8

x = -1 (or) x = 17 **The solution is -1 and 17**