Solve for x 7-2|x-6|=-13

$7 - 2 | x - 6 | = - 13$

Step 1

Move all terms not containing $| x - 6 |$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- 2 | x - 6 | = - 13 - 7$

Subtract $7$ from $- 13$ .

$- 2 | x - 6 | = - 20$

Step 2

Divide each term in $- 2 | x - 6 | = - 20$ by $- 2$ and simplify.

Divide each term in $- 2 | x - 6 | = - 20$ by $- 2$ .

$\frac{- 2 | x - 6 |}{- 2} = \frac{- 20}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | x - 6 |}{- 2} = \frac{- 20}{- 2}$

Divide $| x - 6 |$ by $1$ .

$| x - 6 | = \frac{- 20}{- 2}$

Simplify the right side.

Divide $- 20$ by $- 2$ .

$| x - 6 | = 10$

Step 3

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

$x - 6 = \pm 10$

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.

$x - 6 = 10$

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

Add $6$ to both sides of the equation.

$x = 10 + 6$

Add $10$ and $6$ .

$x = 16$

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

$x - 6 = - 10$

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

Add $6$ to both sides of the equation.

$x = - 10 + 6$

Add $- 10$ and $6$ .

$x = - 4$

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

$x = 16, - 4$