Solve for x 5-5|x+2|=-20

$5 - 5 | x + 2 | = - 20$

Step 1

Move all terms not containing $| x + 2 |$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- 5 | x + 2 | = - 20 - 5$

Subtract $5$ from $- 20$ .

$- 5 | x + 2 | = - 25$

Step 2

Divide each term in $- 5 | x + 2 | = - 25$ by $- 5$ and simplify.

Divide each term in $- 5 | x + 2 | = - 25$ by $- 5$ .

$\frac{- 5 | x + 2 |}{- 5} = \frac{- 25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 | x + 2 |}{- 5} = \frac{- 25}{- 5}$

Divide $| x + 2 |$ by $1$ .

$| x + 2 | = \frac{- 25}{- 5}$

Simplify the right side.

Divide $- 25$ by $- 5$ .

$| x + 2 | = 5$

Step 3

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

$x + 2 = \pm 5$

Step 4

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.

$x + 2 = 5$

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

Subtract $2$ from both sides of the equation.

$x = 5 - 2$

Subtract $2$ from $5$ .

$x = 3$

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

$x + 2 = - 5$

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

Subtract $2$ from both sides of the equation.

$x = - 5 - 2$

Subtract $2$ from $- 5$ .

$x = - 7$

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

$x = 3, - 7$