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

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

Step 1

Combine $\frac{1}{2}$ and $b$ .

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

Step 2

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

Add $\frac{1}{3}$ to both sides of the equation.

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

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

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

Multiply $5$ by $3$ .

$\frac{b}{2} = \frac{2 \cdot 3}{15} + \frac{1}{3} \cdot \frac{5}{5}$

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{b}{2} = \frac{2 \cdot 3}{15} + \frac{5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{b}{2} = \frac{2 \cdot 3}{15} + \frac{5}{15}$

Combine the numerators over the common denominator.

$\frac{b}{2} = \frac{2 \cdot 3 + 5}{15}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{b}{2} = \frac{6 + 5}{15}$

Add $6$ and $5$ .

$\frac{b}{2} = \frac{11}{15}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{b}{2} = 2 (\frac{11}{15})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{b}{2} = 2 (\frac{11}{15})$

Rewrite the expression.

$b = 2 (\frac{11}{15})$

Simplify the right side.

Multiply $2 (\frac{11}{15})$ .

Combine $2$ and $\frac{11}{15}$ .

$b = \frac{2 \cdot 11}{15}$

Multiply $2$ by $11$ .

$b = \frac{22}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{22}{15}$

Decimal Form:

$b = 1.4\overline{6}$

Mixed Number Form:

$b = 1 \frac{7}{15}$

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

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