Finite Math Examples

$\frac{5 x}{2} + \frac{5 y}{4} = \frac{25}{6}$

Step 1

Subtract $\frac{5 x}{2}$ from both sides of the equation.

$\frac{5 y}{4} = \frac{25}{6} - \frac{5 x}{2}$

Step 2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{5} \cdot \frac{5 y}{4}$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3.1.1.2.3

Rewrite the expression.

$y = \frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4}{5} (\frac{25}{6} - \frac{5 x}{2})$ .

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Step 3.2.1.1

Apply the distributive property.

$y = \frac{4}{5} \cdot \frac{25}{6} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{5} \cdot \frac{25}{6} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.2.2

Factor $2$ out of $6$ .

$y = \frac{2 \cdot 2}{5} \cdot \frac{25}{2 \cdot 3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.2.3

Cancel the common factor.

$y = \frac{2 \cdot 2}{5} \cdot \frac{25}{2 \cdot 3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.2.4

Rewrite the expression.

$y = \frac{2}{5} \cdot \frac{25}{3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.3

Cancel the common factor of $5$ .

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Step 3.2.1.3.1

Factor $5$ out of $25$ .

$y = \frac{2}{5} \cdot \frac{5 (5)}{3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.3.2

Cancel the common factor.

$y = \frac{2}{5} \cdot \frac{5 \cdot 5}{3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.3.3

Rewrite the expression.

$y = 2 (\frac{5}{3}) + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.4

Combine $2$ and $\frac{5}{3}$ .

$y = \frac{2 \cdot 5}{3} + \frac{4}{5} (- \frac{5 x}{2})$

Step 3.2.1.5

Multiply $2$ by $5$ .

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

Step 3.2.1.6

Cancel the common factor of $2$ .

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Step 3.2.1.6.1

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

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

Step 3.2.1.6.2

Factor $2$ out of $4$ .

$y = \frac{10}{3} + \frac{2 (2)}{5} \cdot \frac{- 5 x}{2}$

Step 3.2.1.6.3

Cancel the common factor.

$y = \frac{10}{3} + \frac{2 \cdot 2}{5} \cdot \frac{- 5 x}{2}$

Step 3.2.1.6.4

Rewrite the expression.

$y = \frac{10}{3} + \frac{2}{5} (- 5 x)$

Step 3.2.1.7

Cancel the common factor of $5$ .

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Step 3.2.1.7.1

Factor $5$ out of $- 5 x$ .

$y = \frac{10}{3} + \frac{2}{5} (5 (- x))$

Step 3.2.1.7.2

Cancel the common factor.

$y = \frac{10}{3} + \frac{2}{5} (5 (- x))$

Step 3.2.1.7.3

Rewrite the expression.

$y = \frac{10}{3} + 2 (- x)$

Step 3.2.1.8

Multiply $- 1$ by $2$ .

$y = \frac{10}{3} - 2 x$

Step 4

Reorder $\frac{10}{3}$ and $- 2 x$ .

$y = - 2 x + \frac{10}{3}$