Algebra Examples

$| 3 - 6 w | = 39$

Step 1

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

$3 - 6 w = \pm 39$

Step 2

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

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$3 - 6 w = 39$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$- 6 w = 39 - 3$

Step 2.2.2

Subtract $3$ from $39$ .

$- 6 w = 36$

Step 2.3

Divide each term in $- 6 w = 36$ by $- 6$ and simplify.

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Step 2.3.1

Divide each term in $- 6 w = 36$ by $- 6$ .

$\frac{- 6 w}{- 6} = \frac{36}{- 6}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 6$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 6 w}{- 6} = \frac{36}{- 6}$

Step 2.3.2.1.2

Divide $w$ by $1$ .

$w = \frac{36}{- 6}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $36$ by $- 6$ .

$w = - 6$

Step 2.4

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

$3 - 6 w = - 39$

Step 2.5

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

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Step 2.5.1

Subtract $3$ from both sides of the equation.

$- 6 w = - 39 - 3$

Step 2.5.2

Subtract $3$ from $- 39$ .

$- 6 w = - 42$

Step 2.6

Divide each term in $- 6 w = - 42$ by $- 6$ and simplify.

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Step 2.6.1

Divide each term in $- 6 w = - 42$ by $- 6$ .

$\frac{- 6 w}{- 6} = \frac{- 42}{- 6}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $- 6$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{- 6 w}{- 6} = \frac{- 42}{- 6}$

Step 2.6.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 42}{- 6}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 42$ by $- 6$ .

$w = 7$

Step 2.7

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

$w = - 6, 7$