Solve the Absolute Value Inequality for y |(y+9)/4|=5

$| \frac{y + 9}{4} | = 5$

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

$\frac{y + 9}{4} = \pm 5$

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.

$\frac{y + 9}{4} = 5$

Multiply both sides of the equation by $4$ .

$4 \frac{y + 9}{4} = 4 \cdot 5$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{y + 9}{4} = 4 \cdot 5$

Rewrite the expression.

$y + 9 = 4 \cdot 5$

Simplify the right side.

Multiply $4$ by $5$ .

$y + 9 = 20$

Move all terms not containing $y$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$y = 20 - 9$

Subtract $9$ from $20$ .

$y = 11$

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

$\frac{y + 9}{4} = - 5$

Multiply both sides of the equation by $4$ .

$4 \frac{y + 9}{4} = 4 \cdot - 5$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{y + 9}{4} = 4 \cdot - 5$

Rewrite the expression.

$y + 9 = 4 \cdot - 5$

Simplify the right side.

Multiply $4$ by $- 5$ .

$y + 9 = - 20$

Move all terms not containing $y$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$y = - 20 - 9$

Subtract $9$ from $- 20$ .

$y = - 29$

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

$y = 11, - 29$