Solve for y (7y)/8-(3y)/5=11/2

$\frac{7 y}{8} - \frac{3 y}{5} = \frac{11}{2}$

Step 1

Simplify $\frac{7 y}{8} - \frac{3 y}{5}$ .

To write $\frac{7 y}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7 y}{8} \cdot \frac{5}{5} - \frac{3 y}{5} = \frac{11}{2}$

To write $- \frac{3 y}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 y}{8} \cdot \frac{5}{5} - \frac{3 y}{5} \cdot \frac{8}{8} = \frac{11}{2}$

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7 y}{8}$ by $\frac{5}{5}$ .

$\frac{7 y \cdot 5}{8 \cdot 5} - \frac{3 y}{5} \cdot \frac{8}{8} = \frac{11}{2}$

Multiply $8$ by $5$ .

$\frac{7 y \cdot 5}{40} - \frac{3 y}{5} \cdot \frac{8}{8} = \frac{11}{2}$

Multiply $\frac{3 y}{5}$ by $\frac{8}{8}$ .

$\frac{7 y \cdot 5}{40} - \frac{3 y \cdot 8}{5 \cdot 8} = \frac{11}{2}$

Multiply $5$ by $8$ .

$\frac{7 y \cdot 5}{40} - \frac{3 y \cdot 8}{40} = \frac{11}{2}$

Combine the numerators over the common denominator.

$\frac{7 y \cdot 5 - 3 y \cdot 8}{40} = \frac{11}{2}$

Simplify the numerator.

Factor $y$ out of $7 y \cdot 5 - 3 y \cdot 8$ .

Factor $y$ out of $7 y \cdot 5$ .

$\frac{y (7 \cdot 5) - 3 y \cdot 8}{40} = \frac{11}{2}$

Factor $y$ out of $- 3 y \cdot 8$ .

$\frac{y (7 \cdot 5) + y (- 3 \cdot 8)}{40} = \frac{11}{2}$

Factor $y$ out of $y (7 \cdot 5) + y (- 3 \cdot 8)$ .

$\frac{y (7 \cdot 5 - 3 \cdot 8)}{40} = \frac{11}{2}$

Multiply $7$ by $5$ .

$\frac{y (35 - 3 \cdot 8)}{40} = \frac{11}{2}$

Multiply $- 3$ by $8$ .

$\frac{y (35 - 24)}{40} = \frac{11}{2}$

Subtract $24$ from $35$ .

$\frac{y \cdot 11}{40} = \frac{11}{2}$

Move $11$ to the left of $y$ .

$\frac{11 y}{40} = \frac{11}{2}$

Step 2

Multiply both sides of the equation by $\frac{40}{11}$ .

$\frac{40}{11} \cdot \frac{11 y}{40} = \frac{40}{11} \cdot \frac{11}{2}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{40}{11} \cdot \frac{11 y}{40}$ .

Cancel the common factor of $40$ .

Cancel the common factor.

$\frac{40}{11} \cdot \frac{11 y}{40} = \frac{40}{11} \cdot \frac{11}{2}$

Rewrite the expression.

$\frac{1}{11} (11 y) = \frac{40}{11} \cdot \frac{11}{2}$

Cancel the common factor of $11$ .

Factor $11$ out of $11 y$ .

$\frac{1}{11} (11 (y)) = \frac{40}{11} \cdot \frac{11}{2}$

Cancel the common factor.

$\frac{1}{11} (11 y) = \frac{40}{11} \cdot \frac{11}{2}$

Rewrite the expression.

$y = \frac{40}{11} \cdot \frac{11}{2}$

Simplify the right side.

Simplify $\frac{40}{11} \cdot \frac{11}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $40$ .

$y = \frac{2 (20)}{11} \cdot \frac{11}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 20}{11} \cdot \frac{11}{2}$

Rewrite the expression.

$y = \frac{20}{11} \cdot 11$

Cancel the common factor of $11$ .

Cancel the common factor.

$y = \frac{20}{11} \cdot 11$

Rewrite the expression.

$y = 20$

Solve for y (7y)/8-(3y)/5=11/2

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