Trigonometry Examples

$| 6 w + 18 | = 6$

Step 1

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

$6 w + 18 = \pm 6$

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.

$6 w + 18 = 6$

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 $18$ from both sides of the equation.

$6 w = 6 - 18$

Step 2.2.2

Subtract $18$ from $6$ .

$6 w = - 12$

Step 2.3

Divide each term in $6 w = - 12$ by $6$ and simplify.

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Step 2.3.1

Divide each term in $6 w = - 12$ by $6$ .

$\frac{6 w}{6} = \frac{- 12}{6}$

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.

$\frac{6 w}{6} = \frac{- 12}{6}$

Step 2.3.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 12}{6}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 12$ by $6$ .

$w = - 2$

Step 2.4

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

$6 w + 18 = - 6$

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 $18$ from both sides of the equation.

$6 w = - 6 - 18$

Step 2.5.2

Subtract $18$ from $- 6$ .

$6 w = - 24$

Step 2.6

Divide each term in $6 w = - 24$ by $6$ and simplify.

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Step 2.6.1

Divide each term in $6 w = - 24$ by $6$ .

$\frac{6 w}{6} = \frac{- 24}{6}$

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.

$\frac{6 w}{6} = \frac{- 24}{6}$

Step 2.6.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 24}{6}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 24$ by $6$ .

$w = - 4$

Step 2.7

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

$w = - 2, - 4$