Solve for y 12=|y/8|

$12 = | \frac{y}{8} |$

Step 1

Rewrite the equation as $| \frac{y}{8} | = 12$ .

$| \frac{y}{8} | = 12$

Step 2

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

$\frac{y}{8} = \pm 12$

Step 3

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.

$\frac{y}{8} = 12$

Multiply both sides of the equation by $8$ .

$8 \frac{y}{8} = 8 \cdot 12$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{y}{8} = 8 \cdot 12$

Rewrite the expression.

$y = 8 \cdot 12$

Simplify the right side.

Multiply $8$ by $12$ .

$y = 96$

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

$\frac{y}{8} = - 12$

Multiply both sides of the equation by $8$ .

$8 \frac{y}{8} = 8 \cdot - 12$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{y}{8} = 8 \cdot - 12$

Rewrite the expression.

$y = 8 \cdot - 12$

Simplify the right side.

Multiply $8$ by $- 12$ .

$y = - 96$

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

$y = 96, - 96$