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

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

Step 1

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

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

Step 2

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

Add $\frac{1}{6}$ to both sides of the equation.

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$- \frac{b}{3} = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- \frac{b}{3} = \frac{1}{2}$

Step 3

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

$- 3 (- \frac{b}{3}) = - 3 (\frac{1}{2})$

Step 4

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.

$- 3 \frac{- b}{3} = - 3 (\frac{1}{2})$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- b}{3} = - 3 (\frac{1}{2})$

Cancel the common factor.

$3 \cdot - 1 \frac{- b}{3} = - 3 (\frac{1}{2})$

Rewrite the expression.

$- - b = - 3 (\frac{1}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - 3 (\frac{1}{2})$

Multiply $b$ by $1$ .

$b = - 3 (\frac{1}{2})$

Simplify the right side.

Simplify $- 3 (\frac{1}{2})$ .

Combine $- 3$ and $\frac{1}{2}$ .

$b = \frac{- 3}{2}$

Move the negative in front of the fraction.

$b = - \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{3}{2}$

Decimal Form:

$b = - 1.5$

Mixed Number Form:

$b = - 1 \frac{1}{2}$

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

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