Write the Absolute Value as Piecewise |x+24|

$| x + 24 |$

Step 1

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$x + 24 \geq 0$

Step 2

Subtract $24$ from both sides of the inequality.

$x \geq - 24$

Step 3

In the piece where $x + 24$ is non-negative, remove the absolute value.

$x + 24$

Step 4

To find the interval for the second piece, find where the inside of the absolute value is negative.

$x + 24 < 0$

Step 5

Subtract $24$ from both sides of the inequality.

$x < - 24$

Step 6

In the piece where $x + 24$ is negative, remove the absolute value and multiply by $- 1$ .

$- (x + 24)$

Step 7

Write as a piecewise.

${\begin{cases} x + 24 & x \geq - 24 \\ - (x + 24) & x < - 24 \end{cases}$

Step 8

Simplify $- (x + 24)$ .

Apply the distributive property.

${\begin{cases} x + 24 & x \geq - 24 \\ - x - 1 \cdot 24 & x < - 24 \end{cases}$

Multiply $- 1$ by $24$ .

${\begin{cases} x + 24 & x \geq - 24 \\ - x - 24 & x < - 24 \end{cases}$