Solution - Absolute value equations

$$\left(b-7\right)+b=\left(-b+7\right)+b$$

Group like terms:

$$\left(b+b\right)-7=\left(-b+7\right)+b$$

Simplify the arithmetic:

$$2b-7=\left(-b+7\right)+b$$

Group like terms:

$$2b-7=\left(-b+b\right)+7$$

Simplify the arithmetic:

$$2b-7=7$$

Add $$$$ to both sides:

$$\left(2b-7\right)+7=7+7$$

Simplify the arithmetic:

$$2b=7+7$$

Simplify the arithmetic:

$$2b=14$$

Divide both sides by :

$$\frac{\left(2b\right)}{2}=\frac{14}{2}$$

Simplify the fraction:

$$b=\frac{14}{2}$$

Find the greatest common factor of the numerator and denominator:

$$b=\frac{\left(7·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$b=7$$

$$\left(b-7\right)=b-7$$

Subtract $$$$ from both sides:

$$\left(b-7\right)-b=\left(b-7\right)-b$$

Group like terms:

$$\left(b-b\right)-7=\left(b-7\right)-b$$

Simplify the arithmetic:

$$-7=\left(b-7\right)-b$$

Group like terms:

$$-7=\left(b-b\right)-7$$

Simplify the arithmetic:

$$-7=-7$$