Solution - Absolute value equations

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-2x-7=5$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-2x=5+7$$

Simplify the arithmetic:

$$-2x=12$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Move the negative sign from the denominator to the numerator:

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

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:

$$x=-6$$

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$4x-7=-5$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$4x=-5+7$$

Simplify the arithmetic:

$$4x=2$$

Divide both sides by :

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

Simplify the fraction:

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

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:

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