Solution - Absolute value equations

$$\left(w-7\right)-5w=\left(5w+1\right)-5w$$

Group like terms:

$$\left(w-5w\right)-7=\left(5w+1\right)-5w$$

Simplify the arithmetic:

$$-4w-7=\left(5w+1\right)-5w$$

Group like terms:

$$-4w-7=\left(5w-5w\right)+1$$

Simplify the arithmetic:

$$-4w-7=1$$

Add $$$$ to both sides:

$$\left(-4w-7\right)+7=1+7$$

Simplify the arithmetic:

$$-4w=1+7$$

Simplify the arithmetic:

$$-4w=8$$

Divide both sides by :

$$\frac{\left(-4w\right)}{-4}=\frac{8}{-4}$$

Cancel out the negatives:

$$\frac{4w}{4}=\frac{8}{-4}$$

Simplify the fraction:

$$w=\frac{8}{-4}$$

Move the negative sign from the denominator to the numerator:

$$w=\frac{-8}{4}$$

Find the greatest common factor of the numerator and denominator:

$$w=\frac{\left(-2·4\right)}{\left(1·4\right)}$$

Factor out and cancel the greatest common factor:

$$w=-2$$

$$\left(w-7\right)=-5w-1$$

Add $$$$ to both sides:

$$\left(w-7\right)+5w=\left(-5w-1\right)+5w$$

Group like terms:

$$\left(w+5w\right)-7=\left(-5w-1\right)+5w$$

Simplify the arithmetic:

$$6w-7=\left(-5w-1\right)+5w$$

Group like terms:

$$6w-7=\left(-5w+5w\right)-1$$

Simplify the arithmetic:

$$6w-7=-1$$

Add $$$$ to both sides:

$$\left(6w-7\right)+7=-1+7$$

Simplify the arithmetic:

$$6w=-1+7$$

Simplify the arithmetic:

$$6w=6$$

Divide both sides by :

$$\frac{\left(6w\right)}{6}=\frac{6}{6}$$

Simplify the fraction:

$$w=\frac{6}{6}$$

Simplify the fraction:

$$w=1$$