Solve for x 5|x|-8=2

$5 | x | - 8 = 2$

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

Add $8$ to both sides of the equation.

$5 | x | = 2 + 8$

Add $2$ and $8$ .

$5 | x | = 10$

Divide each term in $5 | x | = 10$ by $5$ and simplify.

Divide each term in $5 | x | = 10$ by $5$ .

$\frac{5 | x |}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 | x |}{5} = \frac{10}{5}$

Divide $| x |$ by $1$ .

$| x | = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$| x | = 2$

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

$x = \pm 2$

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

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$