Solution - Absolute value equations

$$\left(-x+5\right)-3x=\left(3x+7\right)-3x$$

Group like terms:

$$\left(-x-3x\right)+5=\left(3x+7\right)-3x$$

Simplify the arithmetic:

$$-4x+5=\left(3x+7\right)-3x$$

Group like terms:

$$-4x+5=\left(3x-3x\right)+7$$

Simplify the arithmetic:

$$-4x+5=7$$

Subtract $$$$ from both sides:

$$\left(-4x+5\right)-5=7-5$$

Simplify the arithmetic:

$$-4x=7-5$$

Simplify the arithmetic:

$$-4x=2$$

Divide both sides by :

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

Cancel out the negatives:

$$\frac{4x}{4}=\frac{2}{-4}$$

Simplify the fraction:

$$x=\frac{2}{-4}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-2}{4}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

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

$$\left(-x+5\right)=-3x-7$$

Add $$$$ to both sides:

$$\left(-x+5\right)+3x=\left(-3x-7\right)+3x$$

Group like terms:

$$\left(-x+3x\right)+5=\left(-3x-7\right)+3x$$

Simplify the arithmetic:

$$2x+5=\left(-3x-7\right)+3x$$

Group like terms:

$$2x+5=\left(-3x+3x\right)-7$$

Simplify the arithmetic:

$$2x+5=-7$$

Subtract $$$$ from both sides:

$$\left(2x+5\right)-5=-7-5$$

Simplify the arithmetic:

$$2x=-7-5$$

Simplify the arithmetic:

$$2x=-12$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{-12}{2}$$

Simplify the fraction:

$$x=\frac{-12}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-6·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-6$$