Solve for b 50=-1/3b+20

$50 = - \frac{1}{3} b + 20$

Step 1

Rewrite the equation as $- \frac{1}{3} b + 20 = 50$ .

$- \frac{1}{3} b + 20 = 50$

Step 2

Combine $b$ and $\frac{1}{3}$ .

$- \frac{b}{3} + 20 = 50$

Step 3

Move all terms not containing $b$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$- \frac{b}{3} = 50 - 20$

Subtract $20$ from $50$ .

$- \frac{b}{3} = 30$

Step 4

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{b}{3}) = - 3 \cdot 30$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{b}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{b}{3}$ into the numerator.

$- 3 \frac{- b}{3} = - 3 \cdot 30$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- b}{3} = - 3 \cdot 30$

Cancel the common factor.

$3 \cdot - 1 \frac{- b}{3} = - 3 \cdot 30$

Rewrite the expression.

$- - b = - 3 \cdot 30$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - 3 \cdot 30$

Multiply $b$ by $1$ .

$b = - 3 \cdot 30$

Simplify the right side.

Multiply $- 3$ by $30$ .

$b = - 90$