Solve for x 4|x-5|=12

$4 | x - 5 | = 12$

Step 1

Divide each term in $4 | x - 5 | = 12$ by $4$ and simplify.

Divide each term in $4 | x - 5 | = 12$ by $4$ .

$\frac{4 | x - 5 |}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 | x - 5 |}{4} = \frac{12}{4}$

Divide $| x - 5 |$ by $1$ .

$| x - 5 | = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$| x - 5 | = 3$

Step 2

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 3

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.

$x - 5 = 3$

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

Add $5$ to both sides of the equation.

$x = 3 + 5$

Add $3$ and $5$ .

$x = 8$

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

$x - 5 = - 3$

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

Add $5$ to both sides of the equation.

$x = - 3 + 5$

Add $- 3$ and $5$ .

$x = 2$

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

$x = 8, 2$