Precalculus Examples

$| \frac{x}{3} | = 1$

Step 1

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

$\frac{x}{3} = \pm 1$

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.

$\frac{x}{3} = 1$

Step 2.2

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot 1$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $3$ .

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Step 2.3.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot 1$

Step 2.3.1.1.2

Rewrite the expression.

$x = 3 \cdot 1$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $3$ by $1$ .

$x = 3$

Step 2.4

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

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

Step 2.5

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot - 1$

Step 2.6

Simplify both sides of the equation.

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Cancel the common factor of $3$ .

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Step 2.6.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot - 1$

Step 2.6.1.1.2

Rewrite the expression.

$x = 3 \cdot - 1$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Multiply $3$ by $- 1$ .

$x = - 3$

Step 2.7

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

$x = 3, - 3$