Algebra Examples

| x - 5 | = 8

$| x - 5 | = 8$

Step 1

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

x - 5 = \pm 8

$x - 5 = \pm 8$

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

$\pm$ to find the first solution.

x - 5 = 8

$x - 5 = 8$

Step 2.2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.2.1

Add

5

$5$ to both sides of the equation.

x = 8 + 5

$x = 8 + 5$

Step 2.2.2

Add

8

$8$ and

5

$5$ .

x = 13

$x = 13$

x = 13

$x = 13$

Step 2.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x - 5 = - 8

$x - 5 = - 8$

Step 2.4

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.4.1

Add

5

$5$ to both sides of the equation.

x = - 8 + 5

$x = - 8 + 5$

Step 2.4.2

Add

- 8

$- 8$ and

5

$5$ .

x = - 3

$x = - 3$

x = - 3

$x = - 3$

Step 2.5

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

x = 13, - 3

$x = 13, - 3$

x = 13, - 3

$x = 13, - 3$