Solve for a |a/5|=12

$| \frac{a}{5} | = 12$

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

$\frac{a}{5} = \pm 12$

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.

$\frac{a}{5} = 12$

Multiply both sides of the equation by $5$ .

$5 \frac{a}{5} = 5 \cdot 12$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{a}{5} = 5 \cdot 12$

Rewrite the expression.

$a = 5 \cdot 12$

Simplify the right side.

Multiply $5$ by $12$ .

$a = 60$

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

$\frac{a}{5} = - 12$

Multiply both sides of the equation by $5$ .

$5 \frac{a}{5} = 5 \cdot - 12$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{a}{5} = 5 \cdot - 12$

Rewrite the expression.

$a = 5 \cdot - 12$

Simplify the right side.

Multiply $5$ by $- 12$ .

$a = - 60$

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

$a = 60, - 60$