Solve the Absolute Value Inequality for x |(5x+20)/4|=5

$| \frac{5 x + 20}{4} | = 5$

Step 1

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

$\frac{5 x + 20}{4} = \pm 5$

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.

$\frac{5 x + 20}{4} = 5$

Multiply both sides by $4$ .

$\frac{5 x + 20}{4} \cdot 4 = 5 \cdot 4$

Simplify.

Simplify the left side.

Simplify $\frac{5 x + 20}{4} \cdot 4$ .

Factor $5$ out of $5 x + 20$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 20}{4} \cdot 4 = 5 \cdot 4$

Factor $5$ out of $20$ .

$\frac{5 x + 5 \cdot 4}{4} \cdot 4 = 5 \cdot 4$

Factor $5$ out of $5 x + 5 \cdot 4$ .

$\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4$

Rewrite the expression.

$5 (x + 4) = 5 \cdot 4$

Apply the distributive property.

$5 x + 5 \cdot 4 = 5 \cdot 4$

Multiply $5$ by $4$ .

$5 x + 20 = 5 \cdot 4$

Simplify the right side.

Multiply $5$ by $4$ .

$5 x + 20 = 20$

Solve for $x$ .

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

Subtract $20$ from both sides of the equation.

$5 x = 20 - 20$

Subtract $20$ from $20$ .

$5 x = 0$

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

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

$\frac{5 x + 20}{4} = - 5$

Multiply both sides by $4$ .

$\frac{5 x + 20}{4} \cdot 4 = - 5 \cdot 4$

Simplify.

Simplify the left side.

Simplify $\frac{5 x + 20}{4} \cdot 4$ .

Factor $5$ out of $5 x + 20$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 20}{4} \cdot 4 = - 5 \cdot 4$

Factor $5$ out of $20$ .

$\frac{5 x + 5 \cdot 4}{4} \cdot 4 = - 5 \cdot 4$

Factor $5$ out of $5 x + 5 \cdot 4$ .

$\frac{5 (x + 4)}{4} \cdot 4 = - 5 \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5 (x + 4)}{4} \cdot 4 = - 5 \cdot 4$

Rewrite the expression.

$5 (x + 4) = - 5 \cdot 4$

Apply the distributive property.

$5 x + 5 \cdot 4 = - 5 \cdot 4$

Multiply $5$ by $4$ .

$5 x + 20 = - 5 \cdot 4$

Simplify the right side.

Multiply $- 5$ by $4$ .

$5 x + 20 = - 20$

Solve for $x$ .

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

Subtract $20$ from both sides of the equation.

$5 x = - 20 - 20$

Subtract $20$ from $- 20$ .

$5 x = - 40$

Divide each term in $5 x = - 40$ by $5$ and simplify.

Divide each term in $5 x = - 40$ by $5$ .

$\frac{5 x}{5} = \frac{- 40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 40}{5}$

Divide $x$ by $1$ .

$x = \frac{- 40}{5}$

Simplify the right side.

Divide $- 40$ by $5$ .

$x = - 8$

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

$x = 0, - 8$

Solve the Absolute Value Inequality for x |(5x+20)/4|=5

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