Solve for w -2|5w-7|+9=-7

$- 2 | 5 w - 7 | + 9 = - 7$

Step 1

Move all terms not containing $| 5 w - 7 |$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$- 2 | 5 w - 7 | = - 7 - 9$

Subtract $9$ from $- 7$ .

$- 2 | 5 w - 7 | = - 16$

Step 2

Divide each term in $- 2 | 5 w - 7 | = - 16$ by $- 2$ and simplify.

Divide each term in $- 2 | 5 w - 7 | = - 16$ by $- 2$ .

$\frac{- 2 | 5 w - 7 |}{- 2} = \frac{- 16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | 5 w - 7 |}{- 2} = \frac{- 16}{- 2}$

Divide $| 5 w - 7 |$ by $1$ .

$| 5 w - 7 | = \frac{- 16}{- 2}$

Simplify the right side.

Divide $- 16$ by $- 2$ .

$| 5 w - 7 | = 8$

Step 3

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

$5 w - 7 = \pm 8$

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.

$5 w - 7 = 8$

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

Add $7$ to both sides of the equation.

$5 w = 8 + 7$

Add $8$ and $7$ .

$5 w = 15$

Divide each term in $5 w = 15$ by $5$ and simplify.

Divide each term in $5 w = 15$ by $5$ .

$\frac{5 w}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{15}{5}$

Divide $w$ by $1$ .

$w = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$w = 3$

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

$5 w - 7 = - 8$

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

Add $7$ to both sides of the equation.

$5 w = - 8 + 7$

Add $- 8$ and $7$ .

$5 w = - 1$

Divide each term in $5 w = - 1$ by $5$ and simplify.

Divide each term in $5 w = - 1$ by $5$ .

$\frac{5 w}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{- 1}{5}$

Divide $w$ by $1$ .

$w = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{1}{5}$

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

$w = 3, - \frac{1}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = 3, - \frac{1}{5}$

Decimal Form:

$w = 3, - 0.2$

Solve for w -2|5w-7|+9=-7

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