Algebra Examples

$\frac{4 y - 11}{15} + \frac{13 - 7 y}{20} = 2$

Step 1

Simplify $\frac{4 y - 11}{15} + \frac{13 - 7 y}{20}$ .

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Step 1.1

To write $\frac{4 y - 11}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4 y - 11}{15} \cdot \frac{4}{4} + \frac{13 - 7 y}{20} = 2$

Step 1.2

To write $\frac{13 - 7 y}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 y - 11}{15} \cdot \frac{4}{4} + \frac{13 - 7 y}{20} \cdot \frac{3}{3} = 2$

Step 1.3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{4 y - 11}{15}$ by $\frac{4}{4}$ .

$\frac{(4 y - 11) \cdot 4}{15 \cdot 4} + \frac{13 - 7 y}{20} \cdot \frac{3}{3} = 2$

Step 1.3.2

Multiply $15$ by $4$ .

$\frac{(4 y - 11) \cdot 4}{60} + \frac{13 - 7 y}{20} \cdot \frac{3}{3} = 2$

Step 1.3.3

Multiply $\frac{13 - 7 y}{20}$ by $\frac{3}{3}$ .

$\frac{(4 y - 11) \cdot 4}{60} + \frac{(13 - 7 y) \cdot 3}{20 \cdot 3} = 2$

Step 1.3.4

Multiply $20$ by $3$ .

$\frac{(4 y - 11) \cdot 4}{60} + \frac{(13 - 7 y) \cdot 3}{60} = 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(4 y - 11) \cdot 4 + (13 - 7 y) \cdot 3}{60} = 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{4 y \cdot 4 - 11 \cdot 4 + (13 - 7 y) \cdot 3}{60} = 2$

Step 1.5.2

Multiply $4$ by $4$ .

$\frac{16 y - 11 \cdot 4 + (13 - 7 y) \cdot 3}{60} = 2$

Step 1.5.3

Multiply $- 11$ by $4$ .

$\frac{16 y - 44 + (13 - 7 y) \cdot 3}{60} = 2$

Step 1.5.4

Apply the distributive property.

$\frac{16 y - 44 + 13 \cdot 3 - 7 y \cdot 3}{60} = 2$

Step 1.5.5

Multiply $13$ by $3$ .

$\frac{16 y - 44 + 39 - 7 y \cdot 3}{60} = 2$

Step 1.5.6

Multiply $3$ by $- 7$ .

$\frac{16 y - 44 + 39 - 21 y}{60} = 2$

Step 1.5.7

Subtract $21 y$ from $16 y$ .

$\frac{- 5 y - 44 + 39}{60} = 2$

Step 1.5.8

Add $- 44$ and $39$ .

$\frac{- 5 y - 5}{60} = 2$

Step 1.5.9

Factor $5$ out of $- 5 y - 5$ .

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Step 1.5.9.1

Factor $5$ out of $- 5 y$ .

$\frac{5 (- y) - 5}{60} = 2$

Step 1.5.9.2

Factor $5$ out of $- 5$ .

$\frac{5 (- y) + 5 (- 1)}{60} = 2$

Step 1.5.9.3

Factor $5$ out of $5 (- y) + 5 (- 1)$ .

$\frac{5 (- y - 1)}{60} = 2$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $5$ out of $60$ .

$\frac{5 (- y - 1)}{5 \cdot 12} = 2$

Step 1.6.2

Cancel the common factor.

$\frac{5 (- y - 1)}{5 \cdot 12} = 2$

Step 1.6.3

Rewrite the expression.

$\frac{- y - 1}{12} = 2$

Step 1.7

Factor $- 1$ out of $- y$ .

$\frac{- (y) - 1}{12} = 2$

Step 1.8

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- (y) - 1 (1)}{12} = 2$

Step 1.9

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

$\frac{- (y + 1)}{12} = 2$

Step 1.10

Simplify the expression.

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Step 1.10.1

Rewrite $- (y + 1)$ as $- 1 (y + 1)$ .

$\frac{- 1 (y + 1)}{12} = 2$

Step 1.10.2

Move the negative in front of the fraction.

$- \frac{y + 1}{12} = 2$

Step 2

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{y + 1}{12}) = - 12 \cdot 2$

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 $- 12 (- \frac{y + 1}{12})$ .

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Step 3.1.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{y + 1}{12}$ into the numerator.

$- 12 \frac{- (y + 1)}{12} = - 12 \cdot 2$

Step 3.1.1.1.2

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- (y + 1)}{12} = - 12 \cdot 2$

Step 3.1.1.1.3

Cancel the common factor.

$12 \cdot - 1 \frac{- (y + 1)}{12} = - 12 \cdot 2$

Step 3.1.1.1.4

Rewrite the expression.

$- - (y + 1) = - 12 \cdot 2$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (y + 1) = - 12 \cdot 2$

Step 3.1.1.2.2

Multiply $y + 1$ by $1$ .

$y + 1 = - 12 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 12$ by $2$ .

$y + 1 = - 24$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$y = - 24 - 1$

Step 4.2

Subtract $1$ from $- 24$ .

$y = - 25$