Basic Math Examples

$\frac{1}{2} \cdot (y + 6) + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1

Simplify $\frac{1}{2} \cdot (y + 6) + 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} y + \frac{1}{2} \cdot 6 + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1.1.2

Combine $\frac{1}{2}$ and $y$ .

$\frac{y}{2} + \frac{1}{2} \cdot 6 + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $6$ .

$\frac{y}{2} + \frac{1}{2} \cdot (2 (3)) + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1.1.3.2

Cancel the common factor.

$\frac{y}{2} + \frac{1}{2} \cdot (2 \cdot 3) + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1.1.3.3

Rewrite the expression.

$\frac{y}{2} + 3 + 4 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 1.2

Add $3$ and $4$ .

$\frac{y}{2} + 7 = \frac{1}{6} \cdot (9 y - 30) - 3$

Step 2

Simplify $\frac{1}{6} \cdot (9 y - 30) - 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{y}{2} + 7 = \frac{1}{6} (9 y) + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.2

Cancel the common factor of $3$ .

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Step 2.1.2.1

Factor $3$ out of $6$ .

$\frac{y}{2} + 7 = \frac{1}{3 (2)} (9 y) + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.2.2

Factor $3$ out of $9 y$ .

$\frac{y}{2} + 7 = \frac{1}{3 (2)} (3 (3 y)) + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.2.3

Cancel the common factor.

$\frac{y}{2} + 7 = \frac{1}{3 \cdot 2} (3 (3 y)) + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.2.4

Rewrite the expression.

$\frac{y}{2} + 7 = \frac{1}{2} (3 y) + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.3

Combine $3$ and $\frac{1}{2}$ .

$\frac{y}{2} + 7 = \frac{3}{2} y + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.4

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

$\frac{y}{2} + 7 = \frac{3 y}{2} + \frac{1}{6} \cdot - 30 - 3$

Step 2.1.5

Cancel the common factor of $6$ .

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Step 2.1.5.1

Factor $6$ out of $- 30$ .

$\frac{y}{2} + 7 = \frac{3 y}{2} + \frac{1}{6} \cdot (6 (- 5)) - 3$

Step 2.1.5.2

Cancel the common factor.

$\frac{y}{2} + 7 = \frac{3 y}{2} + \frac{1}{6} \cdot (6 \cdot - 5) - 3$

Step 2.1.5.3

Rewrite the expression.

$\frac{y}{2} + 7 = \frac{3 y}{2} - 5 - 3$

Step 2.2

Subtract $3$ from $- 5$ .

$\frac{y}{2} + 7 = \frac{3 y}{2} - 8$

Step 3

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

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Step 3.1

Subtract $\frac{3 y}{2}$ from both sides of the equation.

$\frac{y}{2} + 7 - \frac{3 y}{2} = - 8$

Step 3.2

Combine the numerators over the common denominator.

$7 + \frac{y - 3 y}{2} = - 8$

Step 3.3

Subtract $3 y$ from $y$ .

$7 + \frac{- 2 y}{2} = - 8$

Step 3.4

Cancel the common factor of $- 2$ and $2$ .

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Step 3.4.1

Factor $2$ out of $- 2 y$ .

$7 + \frac{2 (- y)}{2} = - 8$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $2$ .

$7 + \frac{2 (- y)}{2 (1)} = - 8$

Step 3.4.2.2

Cancel the common factor.

$7 + \frac{2 (- y)}{2 \cdot 1} = - 8$

Step 3.4.2.3

Rewrite the expression.

$7 + \frac{- y}{1} = - 8$

Step 3.4.2.4

Divide $- y$ by $1$ .

$7 - y = - 8$

Step 4

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

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Step 4.1

Subtract $7$ from both sides of the equation.

$- y = - 8 - 7$

Step 4.2

Subtract $7$ from $- 8$ .

$- y = - 15$

Step 5

Divide each term in $- y = - 15$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- y = - 15$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 15}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 15}{- 1}$

Step 5.2.2

Divide $y$ by $1$ .

$y = \frac{- 15}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 15$ by $- 1$ .

$y = 15$