Solution - Absolute value equations

$$\left(x-4\right)+2x=\left(-2x+5\right)+2x$$

Group like terms:

$$\left(x+2x\right)-4=\left(-2x+5\right)+2x$$

Simplify the arithmetic:

$$3x-4=\left(-2x+5\right)+2x$$

Group like terms:

$$3x-4=\left(-2x+2x\right)+5$$

Simplify the arithmetic:

$$3x-4=5$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$3x=5+4$$

Simplify the arithmetic:

$$3x=9$$

Divide both sides by :

$$\frac{\left(3x\right)}{3}=\frac{9}{3}$$

Simplify the fraction:

$$x=\frac{9}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(3·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=3$$

$$\left(x-4\right)=2x-5$$

Subtract $$$$ from both sides:

$$\left(x-4\right)-2x=\left(2x-5\right)-2x$$

Group like terms:

$$\left(x-2x\right)-4=\left(2x-5\right)-2x$$

Simplify the arithmetic:

$$-x-4=\left(2x-5\right)-2x$$

Group like terms:

$$-x-4=\left(2x-2x\right)-5$$

Simplify the arithmetic:

$$-x-4=-5$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-x=-5+4$$

Simplify the arithmetic:

$$-x=-1$$

Multiply both sides by $$$$:

$$-x·-1=-1·-1$$

Remove the one(s):

$$x=-1·-1$$

Simplify the arithmetic:

$$x=1$$