Trigonometry Examples

$| 3 x + 8 | + 9 = 13$

Step 1

Move all terms not containing $| 3 x + 8 |$ to the right side of the equation.

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Step 1.1

Subtract $9$ from both sides of the equation.

$| 3 x + 8 | = 13 - 9$

Step 1.2

Subtract $9$ from $13$ .

$| 3 x + 8 | = 4$

Step 2

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

$3 x + 8 = \pm 4$

Step 3

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

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Step 3.1

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

$3 x + 8 = 4$

Step 3.2

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

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Step 3.2.1

Subtract $8$ from both sides of the equation.

$3 x = 4 - 8$

Step 3.2.2

Subtract $8$ from $4$ .

$3 x = - 4$

Step 3.3

Divide each term in $3 x = - 4$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 3.4

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

$3 x + 8 = - 4$

Step 3.5

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

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Step 3.5.1

Subtract $8$ from both sides of the equation.

$3 x = - 4 - 8$

Step 3.5.2

Subtract $8$ from $- 4$ .

$3 x = - 12$

Step 3.6

Divide each term in $3 x = - 12$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $- 12$ by $3$ .

$x = - 4$

Step 3.7

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

$x = - \frac{4}{3}, - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}, - 4$

Decimal Form:

$x = - 1.\overline{3}, - 4$

Mixed Number Form:

$x = - 1 \frac{1}{3}, - 4$