Basic Math Examples

$y + \frac{1}{5} \cdot (y - 6) = 18$

Step 1

Simplify $y + \frac{1}{5} \cdot (y - 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$y + \frac{1}{5} y + \frac{1}{5} \cdot - 6 = 18$

Step 1.1.2

Combine $\frac{1}{5}$ and $y$ .

$y + \frac{y}{5} + \frac{1}{5} \cdot - 6 = 18$

Step 1.1.3

Combine $\frac{1}{5}$ and $- 6$ .

$y + \frac{y}{5} + \frac{- 6}{5} = 18$

Step 1.1.4

Move the negative in front of the fraction.

$y + \frac{y}{5} - \frac{6}{5} = 18$

Step 1.2

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

$y \cdot \frac{5}{5} + \frac{y}{5} - \frac{6}{5} = 18$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{y \cdot 5}{5} + \frac{y}{5} - \frac{6}{5} = 18$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{y \cdot 5 + y}{5} - \frac{6}{5} = 18$

Step 1.3.3

Combine the numerators over the common denominator.

$\frac{y \cdot 5 + y - 6}{5} = 18$

Step 1.4

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

$\frac{5 y + y - 6}{5} = 18$

Step 1.5

Simplify terms.

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Step 1.5.1

Add $5 y$ and $y$ .

$\frac{6 y - 6}{5} = 18$

Step 1.5.2

Factor $6$ out of $6 y - 6$ .

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Step 1.5.2.1

Factor $6$ out of $6 y$ .

$\frac{6 (y) - 6}{5} = 18$

Step 1.5.2.2

Factor $6$ out of $- 6$ .

$\frac{6 (y) + 6 (- 1)}{5} = 18$

Step 1.5.2.3

Factor $6$ out of $6 (y) + 6 (- 1)$ .

$\frac{6 (y - 1)}{5} = 18$

Step 2

Multiply both sides of the equation by $\frac{5}{6}$ .

$\frac{5}{6} \cdot \frac{6 (y - 1)}{5} = \frac{5}{6} \cdot 18$

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 $\frac{5}{6} \cdot \frac{6 (y - 1)}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{6} \cdot \frac{6 (y - 1)}{5} = \frac{5}{6} \cdot 18$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{6} (6 (y - 1)) = \frac{5}{6} \cdot 18$

Step 3.1.1.2

Cancel the common factor of $6$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{6} (6 (y - 1)) = \frac{5}{6} \cdot 18$

Step 3.1.1.2.2

Rewrite the expression.

$y - 1 = \frac{5}{6} \cdot 18$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{6} \cdot 18$ .

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Step 3.2.1.1

Cancel the common factor of $6$ .

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Step 3.2.1.1.1

Factor $6$ out of $18$ .

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

Step 3.2.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.3

Rewrite the expression.

$y - 1 = 5 \cdot 3$

Step 3.2.1.2

Multiply $5$ by $3$ .

$y - 1 = 15$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$y = 15 + 1$

Step 4.2

Add $15$ and $1$ .

$y = 16$