Basic Math Examples

$| \frac{z - 6}{5} | = 12$

Step 1

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

$\frac{z - 6}{5} = \pm 12$

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.

$\frac{z - 6}{5} = 12$

Step 2.2

Multiply both sides of the equation by $5$ .

$5 \frac{z - 6}{5} = 5 \cdot 12$

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 $5$ .

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Step 2.3.1.1.1

Cancel the common factor.

$5 \frac{z - 6}{5} = 5 \cdot 12$

Step 2.3.1.1.2

Rewrite the expression.

$z - 6 = 5 \cdot 12$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $5$ by $12$ .

$z - 6 = 60$

Step 2.4

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

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Step 2.4.1

Add $6$ to both sides of the equation.

$z = 60 + 6$

Step 2.4.2

Add $60$ and $6$ .

$z = 66$

Step 2.5

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

$\frac{z - 6}{5} = - 12$

Step 2.6

Multiply both sides of the equation by $5$ .

$5 \frac{z - 6}{5} = 5 \cdot - 12$

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 $5$ .

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Step 2.7.1.1.1

Cancel the common factor.

$5 \frac{z - 6}{5} = 5 \cdot - 12$

Step 2.7.1.1.2

Rewrite the expression.

$z - 6 = 5 \cdot - 12$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply $5$ by $- 12$ .

$z - 6 = - 60$

Step 2.8

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

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Step 2.8.1

Add $6$ to both sides of the equation.

$z = - 60 + 6$

Step 2.8.2

Add $- 60$ and $6$ .

$z = - 54$

Step 2.9

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

$z = 66, - 54$