Solve for b -1/6b+5/6=-1/3

$- \frac{1}{6} b + \frac{5}{6} = - \frac{1}{3}$

Step 1

Combine $b$ and $\frac{1}{6}$ .

$- \frac{b}{6} + \frac{5}{6} = - \frac{1}{3}$

Step 2

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

Subtract $\frac{5}{6}$ from both sides of the equation.

$- \frac{b}{6} = - \frac{1}{3} - \frac{5}{6}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{b}{6} = - \frac{1}{3} \cdot \frac{2}{2} - \frac{5}{6}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$- \frac{b}{6} = - \frac{2}{3 \cdot 2} - \frac{5}{6}$

Multiply $3$ by $2$ .

$- \frac{b}{6} = - \frac{2}{6} - \frac{5}{6}$

Combine the numerators over the common denominator.

$- \frac{b}{6} = \frac{- 2 - 5}{6}$

Subtract $5$ from $- 2$ .

$- \frac{b}{6} = \frac{- 7}{6}$

Move the negative in front of the fraction.

$- \frac{b}{6} = - \frac{7}{6}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- b = - 7$

Step 4

Divide each term in $- b = - 7$ by $- 1$ and simplify.

Divide each term in $- b = - 7$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 7}{- 1}$

Divide $b$ by $1$ .

$b = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$b = 7$