Trigonometry Examples

$| \frac{x}{3} + 2 | = 2$

Step 1

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

$\frac{x}{3} + 2 = \pm 2$

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.

$\frac{x}{3} + 2 = 2$

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$\frac{x}{3} = 2 - 2$

Step 2.2.2

Subtract $2$ from $2$ .

$\frac{x}{3} = 0$

Step 2.3

Set the numerator equal to zero.

$x = 0$

Step 2.4

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

$\frac{x}{3} + 2 = - 2$

Step 2.5

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

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Step 2.5.1

Subtract $2$ from both sides of the equation.

$\frac{x}{3} = - 2 - 2$

Step 2.5.2

Subtract $2$ from $- 2$ .

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

Step 2.6

Multiply both sides of the equation by $3$ .

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

Step 2.7

Simplify both sides of the equation.

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Step 2.7.1

Simplify the left side.

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Step 2.7.1.1

Cancel the common factor of $3$ .

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Step 2.7.1.1.1

Cancel the common factor.

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

Step 2.7.1.1.2

Rewrite the expression.

$x = 3 \cdot - 4$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply $3$ by $- 4$ .

$x = - 12$

Step 2.8

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

$x = 0, - 12$