Solution - Absolute value equations

$$\left(-s+1\right)=s-3$$

Subtract $$$$ from both sides:

$$\left(-s+1\right)-s=\left(s-3\right)-s$$

Group like terms:

$$\left(-s-s\right)+1=\left(s-3\right)-s$$

Simplify the arithmetic:

$$-2s+1=\left(s-3\right)-s$$

Group like terms:

$$-2s+1=\left(s-s\right)-3$$

Simplify the arithmetic:

$$-2s+1=-3$$

Subtract $$$$ from both sides:

$$\left(-2s+1\right)-1=-3-1$$

Simplify the arithmetic:

$$-2s=-3-1$$

Simplify the arithmetic:

$$-2s=-4$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Cancel out the negatives:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$s=2$$

$$\left(-s+1\right)=-s+3$$

Add $$$$ to both sides:

$$\left(-s+1\right)+s=\left(-s+3\right)+s$$

Group like terms:

$$\left(-s+s\right)+1=\left(-s+3\right)+s$$

Simplify the arithmetic:

$$1=\left(-s+3\right)+s$$

Group like terms:

$$1=\left(-s+s\right)+3$$

Simplify the arithmetic:

$$1=3$$

The statement is false:

$$1=3$$