Precalculus Examples

$| x - 5 | = 2$

Step 1

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

$x - 5 = \pm 2$

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.

$x - 5 = 2$

Step 2.2

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

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Step 2.2.1

Add $5$ to both sides of the equation.

$x = 2 + 5$

Step 2.2.2

Add $2$ and $5$ .

$x = 7$

Step 2.3

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

$x - 5 = - 2$

Step 2.4

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

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Step 2.4.1

Add $5$ to both sides of the equation.

$x = - 2 + 5$

Step 2.4.2

Add $- 2$ and $5$ .

$x = 3$

Step 2.5

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

$x = 7, 3$