Solve for w |-7w-9|=8w+3

$| - 7 w - 9 | = 8 w + 3$

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

$- 7 w - 9 = \pm (8 w + 3)$

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.

$- 7 w - 9 = 8 w + 3$

Move all terms containing $w$ to the left side of the equation.

Subtract $8 w$ from both sides of the equation.

$- 7 w - 9 - 8 w = 3$

Subtract $8 w$ from $- 7 w$ .

$- 15 w - 9 = 3$

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

Add $9$ to both sides of the equation.

$- 15 w = 3 + 9$

Add $3$ and $9$ .

$- 15 w = 12$

Divide each term in $- 15 w = 12$ by $- 15$ and simplify.

Divide each term in $- 15 w = 12$ by $- 15$ .

$\frac{- 15 w}{- 15} = \frac{12}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 w}{- 15} = \frac{12}{- 15}$

Divide $w$ by $1$ .

$w = \frac{12}{- 15}$

Simplify the right side.

Cancel the common factor of $12$ and $- 15$ .

Factor $3$ out of $12$ .

$w = \frac{3 (4)}{- 15}$

Cancel the common factors.

Factor $3$ out of $- 15$ .

$w = \frac{3 \cdot 4}{3 \cdot - 5}$

Cancel the common factor.

$w = \frac{3 \cdot 4}{3 \cdot - 5}$

Rewrite the expression.

$w = \frac{4}{- 5}$

Move the negative in front of the fraction.

$w = - \frac{4}{5}$

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

$- 7 w - 9 = - (8 w + 3)$

Simplify $- (8 w + 3)$ .

Rewrite.

$- 7 w - 9 = 0 + 0 - (8 w + 3)$

Simplify by adding zeros.

$- 7 w - 9 = - (8 w + 3)$

Apply the distributive property.

$- 7 w - 9 = - (8 w) - 1 \cdot 3$

Multiply.

Multiply $8$ by $- 1$ .

$- 7 w - 9 = - 8 w - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$- 7 w - 9 = - 8 w - 3$

Move all terms containing $w$ to the left side of the equation.

Add $8 w$ to both sides of the equation.

$- 7 w - 9 + 8 w = - 3$

Add $- 7 w$ and $8 w$ .

$w - 9 = - 3$

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

Add $9$ to both sides of the equation.

$w = - 3 + 9$

Add $- 3$ and $9$ .

$w = 6$

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

$w = - \frac{4}{5}, 6$

Exclude the solutions that do not make $| - 7 w - 9 | = 8 w + 3$ true.

$w = 6$

Solve for w |-7w-9|=8w+3

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