# Simplifying variable expressions

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The absolute value of a number is its distance from zero on a number line.

## Important:

• the absolute value is never negative
• the absolute value of 0 is 0 because the distance between a number and itself is zero.

The absolute value of a number a is written as ∣ a ∣ . For example, the absolute value of – 7 is written as | – 7|.

### Example:

Find the absolute value of 2.

#### Solution:

Graph 2 on a number line

Answer: ∣ 2 ∣ = 2.

## Opposites

Opposites are numbers that are on the opposite side of 0 but have the same absolute value.

To find the opposite of a number, multiply the number by -1, or just add/remove a minus sign.

For example, – 3 and 3 are opposites.

## Negative signs in front of an absolute value

It’s the same thing as a -1 being multiplied by the absolute value of a number.

For example, we can rewrite -|-4| as (-1)|-4|.

In this case, you need to find the absolute value of -4 first, and then multiply that number by -1.

So, -|-4| = (-1) |-4| = (-1) (4) = -4