Solution - Absolute value equations

$$\left(-7x+12\right)-x=\left(x+16\right)-x$$

Group like terms:

$$\left(-7x-x\right)+12=\left(x+16\right)-x$$

Simplify the arithmetic:

$$-8x+12=\left(x+16\right)-x$$

Group like terms:

$$-8x+12=\left(x-x\right)+16$$

Simplify the arithmetic:

$$-8x+12=16$$

Subtract $$$$ from both sides:

$$\left(-8x+12\right)-12=16-12$$

Simplify the arithmetic:

$$-8x=16-12$$

Simplify the arithmetic:

$$-8x=4$$

Divide both sides by :

$$\frac{\left(-8x\right)}{-8}=\frac{4}{-8}$$

Cancel out the negatives:

$$\frac{8x}{8}=\frac{4}{-8}$$

Simplify the fraction:

$$x=\frac{4}{-8}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-4}{8}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-1·4\right)}{\left(2·4\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{-1}{2}$$

$$\left(-7x+12\right)=-x-16$$

Add $$$$ to both sides:

$$\left(-7x+12\right)+x=\left(-x-16\right)+x$$

Group like terms:

$$\left(-7x+x\right)+12=\left(-x-16\right)+x$$

Simplify the arithmetic:

$$-6x+12=\left(-x-16\right)+x$$

Group like terms:

$$-6x+12=\left(-x+x\right)-16$$

Simplify the arithmetic:

$$-6x+12=-16$$

Subtract $$$$ from both sides:

$$\left(-6x+12\right)-12=-16-12$$

Simplify the arithmetic:

$$-6x=-16-12$$

Simplify the arithmetic:

$$-6x=-28$$

Divide both sides by :

$$\frac{\left(-6x\right)}{-6}=\frac{-28}{-6}$$

Cancel out the negatives:

$$\frac{6x}{6}=\frac{-28}{-6}$$

Simplify the fraction:

$$x=\frac{-28}{-6}$$

Cancel out the negatives:

$$x=\frac{28}{6}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(14·2\right)}{\left(3·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{14}{3}$$