Solution - Absolute value equations

$$\left(-5z+3\right)=5z+5·1$$

Simplify the arithmetic:

$$\left(-5z+3\right)=5z+5$$

Subtract $$$$ from both sides:

$$\left(-5z+3\right)-5z=\left(5z+5\right)-5z$$

Group like terms:

$$\left(-5z-5z\right)+3=\left(5z+5\right)-5z$$

Simplify the arithmetic:

$$-10z+3=\left(5z+5\right)-5z$$

Group like terms:

$$-10z+3=\left(5z-5z\right)+5$$

Simplify the arithmetic:

$$-10z+3=5$$

Subtract $$$$ from both sides:

$$\left(-10z+3\right)-3=5-3$$

Simplify the arithmetic:

$$-10z=5-3$$

Simplify the arithmetic:

$$-10z=2$$

Divide both sides by :

$$\frac{\left(-10z\right)}{-10}=\frac{2}{-10}$$

Cancel out the negatives:

$$\frac{10z}{10}=\frac{2}{-10}$$

Simplify the fraction:

$$z=\frac{2}{-10}$$

Move the negative sign from the denominator to the numerator:

$$z=\frac{-2}{10}$$

Find the greatest common factor of the numerator and denominator:

$$z=\frac{\left(-1·2\right)}{\left(5·2\right)}$$

Factor out and cancel the greatest common factor:

$$z=\frac{-1}{5}$$

$$\left(-5z+3\right)=5·\left(-z-1\right)$$

$$\left(-5z+3\right)=5·-z+5·-1$$

Group like terms:

$$\left(-5z+3\right)=\left(5·-1\right)z+5·-1$$

Multiply the coefficients:

$$\left(-5z+3\right)=-5z+5·-1$$

Simplify the arithmetic:

$$\left(-5z+3\right)=-5z-5$$

Add $$$$ to both sides:

$$\left(-5z+3\right)+5z=\left(-5z-5\right)+5z$$

Group like terms:

$$\left(-5z+5z\right)+3=\left(-5z-5\right)+5z$$

Simplify the arithmetic:

$$3=\left(-5z-5\right)+5z$$

Group like terms:

$$3=\left(-5z+5z\right)-5$$

Simplify the arithmetic:

$$3=-5$$

The statement is false:

$$3=-5$$