Solve for a 9=|a/4|

$9 = | \frac{a}{4} |$

Rewrite the equation as $| \frac{a}{4} | = 9$ .

$| \frac{a}{4} | = 9$

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

$\frac{a}{4} = \pm 9$

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.

$\frac{a}{4} = 9$

Multiply both sides of the equation by $4$ .

$4 \frac{a}{4} = 4 \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{a}{4} = 4 \cdot 9$

Rewrite the expression.

$a = 4 \cdot 9$

Simplify the right side.

Multiply $4$ by $9$ .

$a = 36$

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

$\frac{a}{4} = - 9$

Multiply both sides of the equation by $4$ .

$4 \frac{a}{4} = 4 \cdot - 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{a}{4} = 4 \cdot - 9$

Rewrite the expression.

$a = 4 \cdot - 9$

Simplify the right side.

Multiply $4$ by $- 9$ .

$a = - 36$

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

$a = 36, - 36$