Basic Math Examples

$\frac{y + 7}{4} - \frac{y - 11}{5} = 3$

Step 1

Simplify $\frac{y + 7}{4} - \frac{y - 11}{5}$ .

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Step 1.1

To write $\frac{y + 7}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y + 7}{4} \cdot \frac{5}{5} - \frac{y - 11}{5} = 3$

Step 1.2

To write $- \frac{y - 11}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y + 7}{4} \cdot \frac{5}{5} - \frac{y - 11}{5} \cdot \frac{4}{4} = 3$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{y + 7}{4}$ by $\frac{5}{5}$ .

$\frac{(y + 7) \cdot 5}{4 \cdot 5} - \frac{y - 11}{5} \cdot \frac{4}{4} = 3$

Step 1.3.2

Multiply $4$ by $5$ .

$\frac{(y + 7) \cdot 5}{20} - \frac{y - 11}{5} \cdot \frac{4}{4} = 3$

Step 1.3.3

Multiply $\frac{y - 11}{5}$ by $\frac{4}{4}$ .

$\frac{(y + 7) \cdot 5}{20} - \frac{(y - 11) \cdot 4}{5 \cdot 4} = 3$

Step 1.3.4

Multiply $5$ by $4$ .

$\frac{(y + 7) \cdot 5}{20} - \frac{(y - 11) \cdot 4}{20} = 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(y + 7) \cdot 5 - (y - 11) \cdot 4}{20} = 3$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{y \cdot 5 + 7 \cdot 5 - (y - 11) \cdot 4}{20} = 3$

Step 1.5.2

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

$\frac{5 \cdot y + 7 \cdot 5 - (y - 11) \cdot 4}{20} = 3$

Step 1.5.3

Multiply $7$ by $5$ .

$\frac{5 \cdot y + 35 - (y - 11) \cdot 4}{20} = 3$

Step 1.5.4

Apply the distributive property.

$\frac{5 y + 35 + (- y - - 11) \cdot 4}{20} = 3$

Step 1.5.5

Multiply $- 1$ by $- 11$ .

$\frac{5 y + 35 + (- y + 11) \cdot 4}{20} = 3$

Step 1.5.6

Apply the distributive property.

$\frac{5 y + 35 - y \cdot 4 + 11 \cdot 4}{20} = 3$

Step 1.5.7

Multiply $4$ by $- 1$ .

$\frac{5 y + 35 - 4 y + 11 \cdot 4}{20} = 3$

Step 1.5.8

Multiply $11$ by $4$ .

$\frac{5 y + 35 - 4 y + 44}{20} = 3$

Step 1.5.9

Subtract $4 y$ from $5 y$ .

$\frac{y + 35 + 44}{20} = 3$

Step 1.5.10

Add $35$ and $44$ .

$\frac{y + 79}{20} = 3$

Step 2

Multiply both sides of the equation by $20$ .

$20 \frac{y + 79}{20} = 20 \cdot 3$

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

Cancel the common factor of $20$ .

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Step 3.1.1.1

Cancel the common factor.

$20 \frac{y + 79}{20} = 20 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$y + 79 = 20 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $20$ by $3$ .

$y + 79 = 60$

Step 4

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

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Step 4.1

Subtract $79$ from both sides of the equation.

$y = 60 - 79$

Step 4.2

Subtract $79$ from $60$ .

$y = - 19$