Calculus Examples

$| x - 5 | = 6$

Step 1

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

$x - 5 = \pm 6$

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.

$x - 5 = 6$

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.

$x = 6 + 5$

Step 2.2.2

Add $6$ and $5$ .

$x = 11$

Step 2.3

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

$x - 5 = - 6$

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.

$x = - 6 + 5$

Step 2.4.2

Add $- 6$ and $5$ .

$x = - 1$

Step 2.5

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

$x = 11, - 1$