Solve for m -3|9m+2|+10=10

$- 3 | 9 m + 2 | + 10 = 10$

Move all terms not containing $| 9 m + 2 |$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$- 3 | 9 m + 2 | = 10 - 10$

Subtract $10$ from $10$ .

$- 3 | 9 m + 2 | = 0$

Divide each term in $- 3 | 9 m + 2 | = 0$ by $- 3$ and simplify.

Divide each term in $- 3 | 9 m + 2 | = 0$ by $- 3$ .

$\frac{- 3 | 9 m + 2 |}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 | 9 m + 2 |}{- 3} = \frac{0}{- 3}$

Divide $| 9 m + 2 |$ by $1$ .

$| 9 m + 2 | = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$| 9 m + 2 | = 0$

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

$9 m + 2 = \pm 0$

Plus or minus $0$ is $0$ .

$9 m + 2 = 0$

Subtract $2$ from both sides of the equation.

$9 m = - 2$

Divide each term in $9 m = - 2$ by $9$ and simplify.

Divide each term in $9 m = - 2$ by $9$ .

$\frac{9 m}{9} = \frac{- 2}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 m}{9} = \frac{- 2}{9}$

Divide $m$ by $1$ .

$m = \frac{- 2}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{2}{9}$

Decimal Form:

$m = - 0.\overline{2}$