Solve for x |4x|=20

$| 4 x | = 20$

Step 1

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

$4 x = \pm 20$

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.

$4 x = 20$

Divide each term in $4 x = 20$ by $4$ and simplify.

Divide each term in $4 x = 20$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$

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

$4 x = - 20$

Divide each term in $4 x = - 20$ by $4$ and simplify.

Divide each term in $4 x = - 20$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 20$ by $4$ .

$x = - 5$

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

$x = 5, - 5$