Basic Math Examples

$| z + 5 | = 7$

Step 1

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

$z + 5 = \pm 7$

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.

$z + 5 = 7$

Step 2.2

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

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Step 2.2.1

Subtract $5$ from both sides of the equation.

$z = 7 - 5$

Step 2.2.2

Subtract $5$ from $7$ .

$z = 2$

Step 2.3

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

$z + 5 = - 7$

Step 2.4

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

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Step 2.4.1

Subtract $5$ from both sides of the equation.

$z = - 7 - 5$

Step 2.4.2

Subtract $5$ from $- 7$ .

$z = - 12$

Step 2.5

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

$z = 2, - 12$