Solve for a -8-5|-2+9a|=-8

$- 8 - 5 | - 2 + 9 a | = - 8$

Step 1

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

Add $8$ to both sides of the equation.

$- 5 | - 2 + 9 a | = - 8 + 8$

Add $- 8$ and $8$ .

$- 5 | - 2 + 9 a | = 0$

Step 2

Divide each term in $- 5 | - 2 + 9 a | = 0$ by $- 5$ and simplify.

Divide each term in $- 5 | - 2 + 9 a | = 0$ by $- 5$ .

$\frac{- 5 | - 2 + 9 a |}{- 5} = \frac{0}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 | - 2 + 9 a |}{- 5} = \frac{0}{- 5}$

Divide $| - 2 + 9 a |$ by $1$ .

$| - 2 + 9 a | = \frac{0}{- 5}$

Simplify the right side.

Divide $0$ by $- 5$ .

$| - 2 + 9 a | = 0$

Step 3

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

$- 2 + 9 a = \pm 0$

Step 4

Plus or minus $0$ is $0$ .

$- 2 + 9 a = 0$

Step 5

Add $2$ to both sides of the equation.

$9 a = 2$

Step 6

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

Divide each term in $9 a = 2$ by $9$ .

$\frac{9 a}{9} = \frac{2}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 a}{9} = \frac{2}{9}$

Divide $a$ by $1$ .

$a = \frac{2}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{2}{9}$

Decimal Form:

$a = 0.\overline{2}$