Solution - Absolute value equations

$$\left(-x+1\right)-5x=\left(5x+4\right)-5x$$

Group like terms:

$$\left(-x-5x\right)+1=\left(5x+4\right)-5x$$

Simplify the arithmetic:

$$-6x+1=\left(5x+4\right)-5x$$

Group like terms:

$$-6x+1=\left(5x-5x\right)+4$$

Simplify the arithmetic:

$$-6x+1=4$$

Subtract $$$$ from both sides:

$$\left(-6x+1\right)-1=4-1$$

Simplify the arithmetic:

$$-6x=4-1$$

Simplify the arithmetic:

$$-6x=3$$

Divide both sides by :

$$\frac{\left(-6x\right)}{-6}=\frac{3}{-6}$$

Cancel out the negatives:

$$\frac{6x}{6}=\frac{3}{-6}$$

Simplify the fraction:

$$x=\frac{3}{-6}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-3}{6}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-1·3\right)}{\left(2·3\right)}$$

Factor out and cancel the greatest common factor:

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

$$\left(-x+1\right)=-5x-4$$

Add $$$$ to both sides:

$$\left(-x+1\right)+5x=\left(-5x-4\right)+5x$$

Group like terms:

$$\left(-x+5x\right)+1=\left(-5x-4\right)+5x$$

Simplify the arithmetic:

$$4x+1=\left(-5x-4\right)+5x$$

Group like terms:

$$4x+1=\left(-5x+5x\right)-4$$

Simplify the arithmetic:

$$4x+1=-4$$

Subtract $$$$ from both sides:

$$\left(4x+1\right)-1=-4-1$$

Simplify the arithmetic:

$$4x=-4-1$$

Simplify the arithmetic:

$$4x=-5$$

Divide both sides by :

$$\frac{\left(4x\right)}{4}=\frac{-5}{4}$$

Simplify the fraction:

$$x=\frac{-5}{4}$$