Solve for y 2/3y-2/5=5

$\frac{2}{3} y - \frac{2}{5} = 5$

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

$\frac{2 y}{3} - \frac{2}{5} = 5$

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

Add $\frac{2}{5}$ to both sides of the equation.

$\frac{2 y}{3} = 5 + \frac{2}{5}$

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

$\frac{2 y}{3} = 5 \cdot \frac{5}{5} + \frac{2}{5}$

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

$\frac{2 y}{3} = \frac{5 \cdot 5}{5} + \frac{2}{5}$

Combine the numerators over the common denominator.

$\frac{2 y}{3} = \frac{5 \cdot 5 + 2}{5}$

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{2 y}{3} = \frac{25 + 2}{5}$

Add $25$ and $2$ .

$\frac{2 y}{3} = \frac{27}{5}$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot \frac{27}{5}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot \frac{27}{5}$

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot \frac{27}{5}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} \cdot \frac{27}{5}$

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot \frac{27}{5}$

Rewrite the expression.

$y = \frac{3}{2} \cdot \frac{27}{5}$

Simplify the right side.

Multiply $\frac{3}{2} \cdot \frac{27}{5}$ .

Multiply $\frac{3}{2}$ by $\frac{27}{5}$ .

$y = \frac{3 \cdot 27}{2 \cdot 5}$

Multiply $3$ by $27$ .

$y = \frac{81}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{81}{10}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{81}{10}$

Decimal Form:

$y = 8.1$

Mixed Number Form:

$y = 8 \frac{1}{10}$

Solve for y 2/3y-2/5=5

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