Solve for y (7+8y)/15-8/3=(2y)/5

$\frac{7 + 8 y}{15} - \frac{8}{3} = \frac{2 y}{5}$

Multiply both sides by $5$ .

$(\frac{7 + 8 y}{15} - \frac{8}{3}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Simplify.

Simplify the left side.

Simplify $(\frac{7 + 8 y}{15} - \frac{8}{3}) \cdot 5$ .

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

$(\frac{7 + 8 y}{15} - \frac{8}{3} \cdot \frac{5}{5}) \cdot 5 = \frac{2 y}{5} \cdot 5$

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

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

$(\frac{7 + 8 y}{15} - \frac{8 \cdot 5}{3 \cdot 5}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Multiply $3$ by $5$ .

$(\frac{7 + 8 y}{15} - \frac{8 \cdot 5}{15}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Combine the numerators over the common denominator.

$\frac{7 + 8 y - 8 \cdot 5}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Simplify the numerator.

Multiply $- 8$ by $5$ .

$\frac{7 + 8 y - 40}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Subtract $40$ from $7$ .

$\frac{8 y - 33}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{8 y - 33}{5 (3)} \cdot 5 = \frac{2 y}{5} \cdot 5$

Cancel the common factor.

$\frac{8 y - 33}{5 \cdot 3} \cdot 5 = \frac{2 y}{5} \cdot 5$

Rewrite the expression.

$\frac{8 y - 33}{3} = \frac{2 y}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{8 y - 33}{3} = \frac{2 y}{5} \cdot 5$

Rewrite the expression.

$\frac{8 y - 33}{3} = 2 y$

Solve for $y$ .

Multiply both sides by $3$ .

$\frac{8 y - 33}{3} \cdot 3 = 2 y \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{8 y - 33}{3} \cdot 3 = 2 y \cdot 3$

Rewrite the expression.

$8 y - 33 = 2 y \cdot 3$

Simplify the right side.

Multiply $3$ by $2$ .

$8 y - 33 = 6 y$

Solve for $y$ .

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

Subtract $6 y$ from both sides of the equation.

$8 y - 33 - 6 y = 0$

Subtract $6 y$ from $8 y$ .

$2 y - 33 = 0$

Add $33$ to both sides of the equation.

$2 y = 33$

Divide each term in $2 y = 33$ by $2$ and simplify.

Divide each term in $2 y = 33$ by $2$ .

$\frac{2 y}{2} = \frac{33}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{33}{2}$

Divide $y$ by $1$ .

$y = \frac{33}{2}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{33}{2}$

Decimal Form:

$y = 16.5$

Mixed Number Form:

$y = 16 \frac{1}{2}$

Solve for y (7+8y)/15-8/3=(2y)/5

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