Basic Math Examples

$\frac{1}{3} \cdot (y + 10) = 2 y - 5 (y - 6)$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 y - 5 (y - 6) = \frac{1}{3} \cdot (y + 10)$

Step 2

Simplify $2 y - 5 (y - 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 y - 5 y - 5 \cdot - 6 = \frac{1}{3} \cdot (y + 10)$

Step 2.1.2

Multiply $- 5$ by $- 6$ .

$2 y - 5 y + 30 = \frac{1}{3} \cdot (y + 10)$

Step 2.2

Subtract $5 y$ from $2 y$ .

$- 3 y + 30 = \frac{1}{3} \cdot (y + 10)$

Step 3

Simplify $\frac{1}{3} \cdot (y + 10)$ .

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Step 3.1

Apply the distributive property.

$- 3 y + 30 = \frac{1}{3} y + \frac{1}{3} \cdot 10$

Step 3.2

Combine $\frac{1}{3}$ and $y$ .

$- 3 y + 30 = \frac{y}{3} + \frac{1}{3} \cdot 10$

Step 3.3

Combine $\frac{1}{3}$ and $10$ .

$- 3 y + 30 = \frac{y}{3} + \frac{10}{3}$

Step 4

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

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Step 4.1

Subtract $\frac{y}{3}$ from both sides of the equation.

$- 3 y + 30 - \frac{y}{3} = \frac{10}{3}$

Step 4.2

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

$- 3 y \cdot \frac{3}{3} - \frac{y}{3} + 30 = \frac{10}{3}$

Step 4.3

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

$\frac{- 3 y \cdot 3}{3} - \frac{y}{3} + 30 = \frac{10}{3}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{- 3 y \cdot 3 - y}{3} + 30 = \frac{10}{3}$

Step 4.5

Simplify each term.

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Step 4.5.1

Simplify the numerator.

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Step 4.5.1.1

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

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Step 4.5.1.1.1

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

$\frac{y (- 3 \cdot 3) - y}{3} + 30 = \frac{10}{3}$

Step 4.5.1.1.2

Factor $y$ out of $- y$ .

$\frac{y (- 3 \cdot 3) + y \cdot - 1}{3} + 30 = \frac{10}{3}$

Step 4.5.1.1.3

Factor $y$ out of $y (- 3 \cdot 3) + y \cdot - 1$ .

$\frac{y (- 3 \cdot 3 - 1)}{3} + 30 = \frac{10}{3}$

Step 4.5.1.2

Multiply $- 3$ by $3$ .

$\frac{y (- 9 - 1)}{3} + 30 = \frac{10}{3}$

Step 4.5.1.3

Subtract $1$ from $- 9$ .

$\frac{y \cdot - 10}{3} + 30 = \frac{10}{3}$

Step 4.5.2

Move $- 10$ to the left of $y$ .

$\frac{- 10 \cdot y}{3} + 30 = \frac{10}{3}$

Step 4.5.3

Move the negative in front of the fraction.

$- \frac{10 y}{3} + 30 = \frac{10}{3}$

Step 5

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

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Step 5.1

Subtract $30$ from both sides of the equation.

$- \frac{10 y}{3} = \frac{10}{3} - 30$

Step 5.2

To write $- 30$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{10 y}{3} = \frac{10}{3} - 30 \cdot \frac{3}{3}$

Step 5.3

Combine $- 30$ and $\frac{3}{3}$ .

$- \frac{10 y}{3} = \frac{10}{3} + \frac{- 30 \cdot 3}{3}$

Step 5.4

Combine the numerators over the common denominator.

$- \frac{10 y}{3} = \frac{10 - 30 \cdot 3}{3}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 30$ by $3$ .

$- \frac{10 y}{3} = \frac{10 - 90}{3}$

Step 5.5.2

Subtract $90$ from $10$ .

$- \frac{10 y}{3} = \frac{- 80}{3}$

Step 5.6

Move the negative in front of the fraction.

$- \frac{10 y}{3} = - \frac{80}{3}$

Step 6

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 10 y = - 80$

Step 7

Divide each term in $- 10 y = - 80$ by $- 10$ and simplify.

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Step 7.1

Divide each term in $- 10 y = - 80$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 80}{- 10}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 10$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 80}{- 10}$

Step 7.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 80}{- 10}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 80$ by $- 10$ .

$y = 8$