Solve for w |8w+5|=21

$| 8 w + 5 | = 21$

Step 1

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

$8 w + 5 = \pm 21$

Step 2

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.

$8 w + 5 = 21$

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

Subtract $5$ from both sides of the equation.

$8 w = 21 - 5$

Subtract $5$ from $21$ .

$8 w = 16$

Divide each term in $8 w = 16$ by $8$ and simplify.

Divide each term in $8 w = 16$ by $8$ .

$\frac{8 w}{8} = \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 w}{8} = \frac{16}{8}$

Divide $w$ by $1$ .

$w = \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$w = 2$

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

$8 w + 5 = - 21$

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

Subtract $5$ from both sides of the equation.

$8 w = - 21 - 5$

Subtract $5$ from $- 21$ .

$8 w = - 26$

Divide each term in $8 w = - 26$ by $8$ and simplify.

Divide each term in $8 w = - 26$ by $8$ .

$\frac{8 w}{8} = \frac{- 26}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 w}{8} = \frac{- 26}{8}$

Divide $w$ by $1$ .

$w = \frac{- 26}{8}$

Simplify the right side.

Cancel the common factor of $- 26$ and $8$ .

Factor $2$ out of $- 26$ .

$w = \frac{2 (- 13)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$w = \frac{2 \cdot - 13}{2 \cdot 4}$

Cancel the common factor.

$w = \frac{2 \cdot - 13}{2 \cdot 4}$

Rewrite the expression.

$w = \frac{- 13}{4}$

Move the negative in front of the fraction.

$w = - \frac{13}{4}$

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

$w = 2, - \frac{13}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$w = 2, - \frac{13}{4}$

Decimal Form:

$w = 2, - 3.25$

Mixed Number Form:

$w = 2, - 3 \frac{1}{4}$

Solve for w |8w+5|=21

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