Definition of absolute value: the absolute value of a number is the distance the number is from zero

Look at the following two graphs:

We write |6| = 6

The second one shows -8 located at a distance of 8 units from zero.

We write |-8| = 8

Therefore, do not write |5| = -5 or |4| = -4 please!

|6| means distance from 0 to 6

|-8| means distance from 0 to -8

For |-8| = 8, you could also argue that to get 8, you have to take the negative of -8 since - - 8 = 8

So, | - 8| = - - 8 = 8

This observation helps us to come up with a formal definition of absolute value

This definition is important to understand before solving absolute value equations or absolute value inequalities

Calculate the absolute value of the following numerical expressions

1) 4

2) -5 + 5 × 2 − 15

3) -8 + 2 × 5

| -8 + 2 × 5 | = | -8 + 10 |

| -8 + 2 × 5 | = | 2 |

| -8 + 2 × 5 | = 2

| 4

| 4

| 4

| 4

|-5 + 5 × 2 − 15| = | -5 + 10 − 15 |

|(-5 + 5 × 2 − 15)| = | 5 − 15 |

|(-5 + 5 × 2 − 15)| = | -15 |

|(-5 + 5 × 2 − 15)| = 15