Solve for a |-3a|=24

$| - 3 a | = 24$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$- 3 a = \pm 24$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$- 3 a = 24$

Divide each term in $- 3 a = 24$ by $- 3$ and simplify.

Divide each term in $- 3 a = 24$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{24}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 a}{- 3} = \frac{24}{- 3}$

Divide $a$ by $1$ .

$a = \frac{24}{- 3}$

Simplify the right side.

Divide $24$ by $- 3$ .

$a = - 8$

Next, use the negative value of the $\pm$ to find the second solution.

$- 3 a = - 24$

Divide each term in $- 3 a = - 24$ by $- 3$ and simplify.

Divide each term in $- 3 a = - 24$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{- 24}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 a}{- 3} = \frac{- 24}{- 3}$

Divide $a$ by $1$ .

$a = \frac{- 24}{- 3}$

Simplify the right side.

Divide $- 24$ by $- 3$ .

$a = 8$

The complete solution is the result of both the positive and negative portions of the solution.

$a = - 8, 8$