Precalculus Examples

$\frac{2}{5} (y + 10) = 8$

Step 1

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} (\frac{2}{5} \cdot (y + 10)) = \frac{5}{2} \cdot 8$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5}{2} (\frac{2}{5} \cdot (y + 10))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{5}{2} (\frac{2}{5} y + \frac{2}{5} \cdot 10) = \frac{5}{2} \cdot 8$

Step 2.1.1.2

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

$\frac{5}{2} (\frac{2 y}{5} + \frac{2}{5} \cdot 10) = \frac{5}{2} \cdot 8$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Factor $5$ out of $10$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Multiply $2$ by $2$ .

$\frac{5}{2} (\frac{2 y}{5} + 4) = \frac{5}{2} \cdot 8$

Step 2.1.1.5

Apply the distributive property.

$\frac{5}{2} \cdot \frac{2 y}{5} + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 y}{5} + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{2} (2 y) + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{2} (2 y) + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.7.3

Rewrite the expression.

$y + \frac{5}{2} \cdot 4 = \frac{5}{2} \cdot 8$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $4$ .

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

Step 2.1.1.8.2

Cancel the common factor.

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

Step 2.1.1.8.3

Rewrite the expression.

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

Step 2.1.1.9

Multiply $5$ by $2$ .

$y + 10 = \frac{5}{2} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{2} \cdot 8$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $8$ .

$y + 10 = \frac{5}{2} \cdot (2 (4))$

Step 2.2.1.1.2

Cancel the common factor.

$y + 10 = \frac{5}{2} \cdot (2 \cdot 4)$

Step 2.2.1.1.3

Rewrite the expression.

$y + 10 = 5 \cdot 4$

Step 2.2.1.2

Multiply $5$ by $4$ .

$y + 10 = 20$

Step 3

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

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Step 3.1

Subtract $10$ from both sides of the equation.

$y = 20 - 10$

Step 3.2

Subtract $10$ from $20$ .

$y = 10$