Finite Math Examples

$| \frac{n}{4} | = 3$

Step 1

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

$\frac{n}{4} = \pm 3$

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.

$\frac{n}{4} = 3$

Step 2.2

Multiply both sides of the equation by $4$ .

$4 \frac{n}{4} = 4 \cdot 3$

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 $4$ .

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Step 2.3.1.1.1

Cancel the common factor.

$4 \frac{n}{4} = 4 \cdot 3$

Step 2.3.1.1.2

Rewrite the expression.

$n = 4 \cdot 3$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $4$ by $3$ .

$n = 12$

Step 2.4

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

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

Step 2.5

Multiply both sides of the equation by $4$ .

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

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 $4$ .

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Step 2.6.1.1.1

Cancel the common factor.

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

Step 2.6.1.1.2

Rewrite the expression.

$n = 4 \cdot - 3$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Multiply $4$ by $- 3$ .

$n = - 12$

Step 2.7

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

$n = 12, - 12$