Solve for b 3/5b-5+3/2b=2b-4/5

$\frac{3}{5} b - 5 + \frac{3}{2} b = 2 b - \frac{4}{5}$

Simplify $\frac{3}{5} b - 5 + \frac{3}{2} b$ .

Simplify each term.

Combine $\frac{3}{5}$ and $b$ .

$\frac{3 b}{5} - 5 + \frac{3}{2} b = 2 b - \frac{4}{5}$

Combine $\frac{3}{2}$ and $b$ .

$\frac{3 b}{5} - 5 + \frac{3 b}{2} = 2 b - \frac{4}{5}$

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

$\frac{3 b}{5} \cdot \frac{2}{2} + \frac{3 b}{2} - 5 = 2 b - \frac{4}{5}$

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

$\frac{3 b}{5} \cdot \frac{2}{2} + \frac{3 b}{2} \cdot \frac{5}{5} - 5 = 2 b - \frac{4}{5}$

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

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

$\frac{3 b \cdot 2}{5 \cdot 2} + \frac{3 b}{2} \cdot \frac{5}{5} - 5 = 2 b - \frac{4}{5}$

Multiply $5$ by $2$ .

$\frac{3 b \cdot 2}{10} + \frac{3 b}{2} \cdot \frac{5}{5} - 5 = 2 b - \frac{4}{5}$

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

$\frac{3 b \cdot 2}{10} + \frac{3 b \cdot 5}{2 \cdot 5} - 5 = 2 b - \frac{4}{5}$

Multiply $2$ by $5$ .

$\frac{3 b \cdot 2}{10} + \frac{3 b \cdot 5}{10} - 5 = 2 b - \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{3 b \cdot 2 + 3 b \cdot 5}{10} - 5 = 2 b - \frac{4}{5}$

Simplify the numerator.

Factor $3 b$ out of $3 b \cdot 2 + 3 b \cdot 5$ .

Factor $3 b$ out of $3 b \cdot 2$ .

$\frac{3 b (2) + 3 b \cdot 5}{10} - 5 = 2 b - \frac{4}{5}$

Factor $3 b$ out of $3 b \cdot 5$ .

$\frac{3 b (2) + 3 b (5)}{10} - 5 = 2 b - \frac{4}{5}$

Factor $3 b$ out of $3 b (2) + 3 b (5)$ .

$\frac{3 b (2 + 5)}{10} - 5 = 2 b - \frac{4}{5}$

Add $2$ and $5$ .

$\frac{3 b \cdot 7}{10} - 5 = 2 b - \frac{4}{5}$

Multiply $7$ by $3$ .

$\frac{21 b}{10} - 5 = 2 b - \frac{4}{5}$

Move all terms containing $b$ to the left side of the equation.

Subtract $2 b$ from both sides of the equation.

$\frac{21 b}{10} - 5 - 2 b = - \frac{4}{5}$

To write $- 2 b$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{21 b}{10} - 2 b \cdot \frac{10}{10} - 5 = - \frac{4}{5}$

Combine $- 2 b$ and $\frac{10}{10}$ .

$\frac{21 b}{10} + \frac{- 2 b \cdot 10}{10} - 5 = - \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{21 b - 2 b \cdot 10}{10} - 5 = - \frac{4}{5}$

Simplify each term.

Simplify the numerator.

Factor $b$ out of $21 b - 2 b \cdot 10$ .

Factor $b$ out of $21 b$ .

$\frac{b \cdot 21 - 2 b \cdot 10}{10} - 5 = - \frac{4}{5}$

Factor $b$ out of $- 2 b \cdot 10$ .

$\frac{b \cdot 21 + b (- 2 \cdot 10)}{10} - 5 = - \frac{4}{5}$

Factor $b$ out of $b \cdot 21 + b (- 2 \cdot 10)$ .

$\frac{b (21 - 2 \cdot 10)}{10} - 5 = - \frac{4}{5}$

Multiply $- 2$ by $10$ .

$\frac{b (21 - 20)}{10} - 5 = - \frac{4}{5}$

Subtract $20$ from $21$ .

$\frac{b \cdot 1}{10} - 5 = - \frac{4}{5}$

Multiply $b$ by $1$ .

$\frac{b}{10} - 5 = - \frac{4}{5}$

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

Add $5$ to both sides of the equation.

$\frac{b}{10} = - \frac{4}{5} + 5$

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

$\frac{b}{10} = - \frac{4}{5} + 5 \cdot \frac{5}{5}$

Combine $5$ and $\frac{5}{5}$ .

$\frac{b}{10} = - \frac{4}{5} + \frac{5 \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{b}{10} = \frac{- 4 + 5 \cdot 5}{5}$

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{b}{10} = \frac{- 4 + 25}{5}$

Add $- 4$ and $25$ .

$\frac{b}{10} = \frac{21}{5}$

Multiply both sides of the equation by $10$ .

$10 \frac{b}{10} = 10 (\frac{21}{5})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$10 \frac{b}{10} = 10 (\frac{21}{5})$

Rewrite the expression.

$b = 10 (\frac{21}{5})$

Simplify the right side.

Simplify $10 (\frac{21}{5})$ .

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$b = 5 (2) \frac{21}{5}$

Cancel the common factor.

$b = 5 \cdot 2 \frac{21}{5}$

Rewrite the expression.

$b = 2 \cdot 21$

Multiply $2$ by $21$ .

$b = 42$

Solve for b 3/5b-5+3/2b=2b-4/5

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