Solve for m -2|m-2|=-6

$- 2 | m - 2 | = - 6$

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

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

$\frac{- 2 | m - 2 |}{- 2} = \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | m - 2 |}{- 2} = \frac{- 6}{- 2}$

Divide $| m - 2 |$ by $1$ .

$| m - 2 | = \frac{- 6}{- 2}$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$| m - 2 | = 3$

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

$m - 2 = \pm 3$

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.

$m - 2 = 3$

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

Add $2$ to both sides of the equation.

$m = 3 + 2$

Add $3$ and $2$ .

$m = 5$

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

$m - 2 = - 3$

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

Add $2$ to both sides of the equation.

$m = - 3 + 2$

Add $- 3$ and $2$ .

$m = - 1$

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

$m = 5, - 1$