Solve for b 1/5=-3/11b+1/2

$\frac{1}{5} = - \frac{3}{11} b + \frac{1}{2}$

Rewrite the equation as $- \frac{3}{11} b + \frac{1}{2} = \frac{1}{5}$ .

$- \frac{3}{11} b + \frac{1}{2} = \frac{1}{5}$

Simplify each term.

Combine $b$ and $\frac{3}{11}$ .

$- \frac{b \cdot 3}{11} + \frac{1}{2} = \frac{1}{5}$

Move $3$ to the left of $b$ .

$- \frac{3 b}{11} + \frac{1}{2} = \frac{1}{5}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{3 b}{11} = \frac{1}{5} - \frac{1}{2}$

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 b}{11} = \frac{1}{5} \cdot \frac{2}{2} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{3 b}{11} = \frac{1}{5} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{5}{5}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$- \frac{3 b}{11} = \frac{2}{5 \cdot 2} - \frac{1}{2} \cdot \frac{5}{5}$

Multiply $5$ by $2$ .

$- \frac{3 b}{11} = \frac{2}{10} - \frac{1}{2} \cdot \frac{5}{5}$

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$- \frac{3 b}{11} = \frac{2}{10} - \frac{5}{2 \cdot 5}$

Multiply $2$ by $5$ .

$- \frac{3 b}{11} = \frac{2}{10} - \frac{5}{10}$

Combine the numerators over the common denominator.

$- \frac{3 b}{11} = \frac{2 - 5}{10}$

Subtract $5$ from $2$ .

$- \frac{3 b}{11} = \frac{- 3}{10}$

Move the negative in front of the fraction.

$- \frac{3 b}{11} = - \frac{3}{10}$

Multiply both sides of the equation by $- \frac{11}{3}$ .

$- \frac{11}{3} (- \frac{3 b}{11}) = - \frac{11}{3} (- \frac{3}{10})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{11}{3} (- \frac{3 b}{11})$ .

Cancel the common factor of $11$ .

Move the leading negative in $- \frac{11}{3}$ into the numerator.

$\frac{- 11}{3} (- \frac{3 b}{11}) = - \frac{11}{3} (- \frac{3}{10})$

Move the leading negative in $- \frac{3 b}{11}$ into the numerator.

$\frac{- 11}{3} \cdot \frac{- 3 b}{11} = - \frac{11}{3} (- \frac{3}{10})$

Factor $11$ out of $- 11$ .

$\frac{11 (- 1)}{3} \cdot \frac{- 3 b}{11} = - \frac{11}{3} (- \frac{3}{10})$

Cancel the common factor.

$\frac{11 \cdot - 1}{3} \cdot \frac{- 3 b}{11} = - \frac{11}{3} (- \frac{3}{10})$

Rewrite the expression.

$\frac{- 1}{3} (- 3 b) = - \frac{11}{3} (- \frac{3}{10})$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 b$ .

$\frac{- 1}{3} (3 (- b)) = - \frac{11}{3} (- \frac{3}{10})$

Cancel the common factor.

$\frac{- 1}{3} (3 (- b)) = - \frac{11}{3} (- \frac{3}{10})$

Rewrite the expression.

$- - b = - \frac{11}{3} (- \frac{3}{10})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{11}{3} (- \frac{3}{10})$

Multiply $b$ by $1$ .

$b = - \frac{11}{3} (- \frac{3}{10})$

Simplify the right side.

Simplify $- \frac{11}{3} (- \frac{3}{10})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{11}{3}$ into the numerator.

$b = \frac{- 11}{3} (- \frac{3}{10})$

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$b = \frac{- 11}{3} \cdot \frac{- 3}{10}$

Factor $3$ out of $- 3$ .

$b = \frac{- 11}{3} \cdot \frac{3 (- 1)}{10}$

Cancel the common factor.

$b = \frac{- 11}{3} \cdot \frac{3 \cdot - 1}{10}$

Rewrite the expression.

$b = - 11 (\frac{- 1}{10})$

Combine $- 11$ and $\frac{- 1}{10}$ .

$b = \frac{- 11 \cdot - 1}{10}$

Multiply $- 11$ by $- 1$ .

$b = \frac{11}{10}$

The result can be shown in multiple forms.

Exact Form:

$b = \frac{11}{10}$

Decimal Form:

$b = 1.1$

Mixed Number Form:

$b = 1 \frac{1}{10}$

Solve for b 1/5=-3/11b+1/2

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