Solve for y 4/5y-5/3=-5/3y+5

$\frac{4}{5} y - \frac{5}{3} = - \frac{5}{3} y + 5$

Combine $\frac{4}{5}$ and $y$ .

$\frac{4 y}{5} - \frac{5}{3} = - \frac{5}{3} y + 5$

Simplify each term.

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

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

Move $5$ to the left of $y$ .

$\frac{4 y}{5} - \frac{5}{3} = - \frac{5 y}{3} + 5$

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

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Add $\frac{5 y}{3}$ to both sides of the equation.

$\frac{4 y}{5} - \frac{5}{3} + \frac{5 y}{3} = 5$

To write $\frac{4 y}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

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

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Multiply $\frac{4 y}{5}$ and $\frac{3}{3}$ .

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

Multiply $5$ by $3$ .

$\frac{4 y \cdot 3}{15} + \frac{5 y}{3} \cdot \frac{5}{5} - \frac{5}{3} = 5$

Multiply $\frac{5 y}{3}$ and $\frac{5}{5}$ .

$\frac{4 y \cdot 3}{15} + \frac{5 y \cdot 5}{3 \cdot 5} - \frac{5}{3} = 5$

Multiply $3$ by $5$ .

$\frac{4 y \cdot 3}{15} + \frac{5 y \cdot 5}{15} - \frac{5}{3} = 5$

Combine the numerators over the common denominator.

$\frac{4 y \cdot 3 + 5 y \cdot 5}{15} - \frac{5}{3} = 5$

Simplify each term.

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Simplify the numerator.

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Factor $y$ out of $4 y \cdot 3 + 5 y \cdot 5$ .

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Factor $y$ out of $4 y \cdot 3$ .

$\frac{y (4 \cdot 3) + 5 y \cdot 5}{15} - \frac{5}{3} = 5$

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

$\frac{y (4 \cdot 3) + y (5 \cdot 5)}{15} - \frac{5}{3} = 5$

Factor $y$ out of $y (4 \cdot 3) + y (5 \cdot 5)$ .

$\frac{y (4 \cdot 3 + 5 \cdot 5)}{15} - \frac{5}{3} = 5$

Multiply $4$ by $3$ .

$\frac{y (12 + 5 \cdot 5)}{15} - \frac{5}{3} = 5$

Multiply $5$ by $5$ .

$\frac{y (12 + 25)}{15} - \frac{5}{3} = 5$

Add $12$ and $25$ .

$\frac{y \cdot 37}{15} - \frac{5}{3} = 5$

Move $37$ to the left of $y$ .

$\frac{37 y}{15} - \frac{5}{3} = 5$

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

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Add $\frac{5}{3}$ to both sides of the equation.

$\frac{37 y}{15} = 5 + \frac{5}{3}$

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

$\frac{37 y}{15} = 5 \cdot \frac{3}{3} + \frac{5}{3}$

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

$\frac{37 y}{15} = \frac{5 \cdot 3}{3} + \frac{5}{3}$

Combine the numerators over the common denominator.

$\frac{37 y}{15} = \frac{5 \cdot 3 + 5}{3}$

Simplify the numerator.

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Multiply $5$ by $3$ .

$\frac{37 y}{15} = \frac{15 + 5}{3}$

Add $15$ and $5$ .

$\frac{37 y}{15} = \frac{20}{3}$

Multiply both sides of the equation by $\frac{15}{37}$ .

$\frac{15}{37} \cdot \frac{37 y}{15} = \frac{15}{37} \cdot \frac{20}{3}$

Simplify both sides of the equation.

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Simplify $\frac{15}{37} \cdot \frac{37 y}{15}$ .

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Cancel the common factor of $15$ .

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Cancel the common factor.

$\frac{15}{37} \cdot \frac{37 y}{15} = \frac{15}{37} \cdot \frac{20}{3}$

Rewrite the expression.

$\frac{1}{37} \cdot (37 y) = \frac{15}{37} \cdot \frac{20}{3}$

Cancel the common factor of $37$ .

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Factor $37$ out of $37 y$ .

$\frac{1}{37} \cdot (37 (y)) = \frac{15}{37} \cdot \frac{20}{3}$

Cancel the common factor.

$\frac{1}{37} \cdot (37 y) = \frac{15}{37} \cdot \frac{20}{3}$

Rewrite the expression.

$y = \frac{15}{37} \cdot \frac{20}{3}$

Simplify $\frac{15}{37} \cdot \frac{20}{3}$ .

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Cancel the common factor of $3$ .

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Factor $3$ out of $15$ .

$y = \frac{3 (5)}{37} \cdot \frac{20}{3}$

Cancel the common factor.

$y = \frac{3 \cdot 5}{37} \cdot \frac{20}{3}$

Rewrite the expression.

$y = \frac{5}{37} \cdot 20$

Combine $\frac{5}{37}$ and $20$ .

$y = \frac{5 \cdot 20}{37}$

Multiply $5$ by $20$ .

$y = \frac{100}{37}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{100}{37}$

Decimal Form:

$y = 2.\overline{702}$

Mixed Number Form:

$y = 2 \frac{26}{37}$

Solve for y 4/5y-5/3=-5/3y+5

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