Solve for x 4|x-12|+1=-7|x-12|+1

$4 | x - 12 | + 1 = - 7 | x - 12 | + 1$

Move all terms containing $| x - 12 |$ to the left side of the equation.

Add $7 | x - 12 |$ to both sides of the equation.

$4 | x - 12 | + 1 + 7 | x - 12 | = 1$

Add $4 | x - 12 |$ and $7 | x - 12 |$ .

$11 | x - 12 | + 1 = 1$

Move all terms not containing $| x - 12 |$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$11 | x - 12 | = 1 - 1$

Subtract $1$ from $1$ .

$11 | x - 12 | = 0$

Divide each term in $11 | x - 12 | = 0$ by $11$ and simplify.

Divide each term in $11 | x - 12 | = 0$ by $11$ .

$\frac{11 | x - 12 |}{11} = \frac{0}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 | x - 12 |}{11} = \frac{0}{11}$

Divide $| x - 12 |$ by $1$ .

$| x - 12 | = \frac{0}{11}$

Simplify the right side.

Divide $0$ by $11$ .

$| x - 12 | = 0$

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

$x - 12 = \pm 0$

Plus or minus $0$ is $0$ .

$x - 12 = 0$