Pre-Algebra Examples

$| x + 5 | = 3$

Step 1

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

$x + 5 = \pm 3$

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.

$x + 5 = 3$

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 $5$ from both sides of the equation.

$x = 3 - 5$

Step 2.2.2

Subtract $5$ from $3$ .

$x = - 2$

Step 2.3

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

$x + 5 = - 3$

Step 2.4

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

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Step 2.4.1

Subtract $5$ from both sides of the equation.

$x = - 3 - 5$

Step 2.4.2

Subtract $5$ from $- 3$ .

$x = - 8$

Step 2.5

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

$x = - 2, - 8$