Solution - Absolute value equations

$$\left(-3x+\frac{-5}{2}\right)-2x=\left(2x\right)-2x$$

Group like terms:

$$\left(-3x-2x\right)+\frac{-5}{2}=\left(2x\right)-2x$$

Simplify the arithmetic:

$$-5x+\frac{-5}{2}=\left(2x\right)-2x$$

Simplify the arithmetic:

$$-5x+\frac{-5}{2}=0$$

Add $$$$ to both sides:

$$\left(-5x+\frac{-5}{2}\right)+\frac{5}{2}=0+\frac{5}{2}$$

Combine the fractions:

$$-5x+\frac{\left(-5+5\right)}{2}=0+\frac{5}{2}$$

Combine the numerators:

$$-5x+\frac{0}{2}=0+\frac{5}{2}$$

Reduce the zero numerator:

$$-5x+0=0+\frac{5}{2}$$

Simplify the arithmetic:

$$-5x=0+\frac{5}{2}$$

Simplify the arithmetic:

$$-5x=\frac{5}{2}$$

Divide both sides by :

$$\frac{\left(-5x\right)}{-5}=\frac{\left(\frac{5}{2}\right)}{-5}$$

Cancel out the negatives:

$$\frac{5x}{5}=\frac{\left(\frac{5}{2}\right)}{-5}$$

Simplify the fraction:

$$x=\frac{\left(\frac{5}{2}\right)}{-5}$$

Simplify the arithmetic:

$$x=\frac{5}{\left(2·-5\right)}$$

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

$$\left(-3x+\frac{-5}{2}\right)+\frac{5}{2}=\left(-2x\right)+\frac{5}{2}$$

Combine the fractions:

$$-3x+\frac{\left(-5+5\right)}{2}=\left(-2x\right)+\frac{5}{2}$$

Combine the numerators:

$$-3x+\frac{0}{2}=\left(-2x\right)+\frac{5}{2}$$

Reduce the zero numerator:

$$-3x+0=\left(-2x\right)+\frac{5}{2}$$

Simplify the arithmetic:

$$-3x=\left(-2x\right)+\frac{5}{2}$$

Add $$$$ to both sides:

$$\left(-3x\right)+2x=\left(\left(-2x\right)+\frac{5}{2}\right)+2x$$

Simplify the arithmetic:

$$-x=\left(\left(-2x\right)+\frac{5}{2}\right)+2x$$

Group like terms:

$$-x=\left(-2x+2x\right)+\frac{5}{2}$$

Simplify the arithmetic:

$$-x=\frac{5}{2}$$

Multiply both sides by $$$$:

$$-x·-1=\left(\frac{5}{2}\right)·-1$$

Remove the one(s):

$$x=\left(\frac{5}{2}\right)·-1$$

Remove the one(s):

$$x=\frac{-5}{2}$$