Solve for y y/4-(y+1)/5=(y+2)/8

$\frac{y}{4} - \frac{y + 1}{5} = \frac{y + 2}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{y}{4} - \frac{y + 1}{5}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{y}{4} - \frac{y + 1}{5}) \cdot 8$ .

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

$(\frac{y}{4} \cdot \frac{5}{5} - \frac{y + 1}{5}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

To write $- \frac{y + 1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{y}{4} \cdot \frac{5}{5} - \frac{y + 1}{5} \cdot \frac{4}{4}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

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

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

$(\frac{y \cdot 5}{4 \cdot 5} - \frac{y + 1}{5} \cdot \frac{4}{4}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $4$ by $5$ .

$(\frac{y \cdot 5}{20} - \frac{y + 1}{5} \cdot \frac{4}{4}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $\frac{y + 1}{5}$ by $\frac{4}{4}$ .

$(\frac{y \cdot 5}{20} - \frac{(y + 1) \cdot 4}{5 \cdot 4}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $5$ by $4$ .

$(\frac{y \cdot 5}{20} - \frac{(y + 1) \cdot 4}{20}) \cdot 8 = \frac{y + 2}{8} \cdot 8$

Combine the numerators over the common denominator.

$\frac{y \cdot 5 - (y + 1) \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Simplify the numerator.

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

$\frac{5 \cdot y - (y + 1) \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Apply the distributive property.

$\frac{5 y + (- y - 1 \cdot 1) \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $- 1$ by $1$ .

$\frac{5 y + (- y - 1) \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Apply the distributive property.

$\frac{5 y - y \cdot 4 - 1 \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $4$ by $- 1$ .

$\frac{5 y - 4 y - 1 \cdot 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Multiply $- 1$ by $4$ .

$\frac{5 y - 4 y - 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Subtract $4 y$ from $5 y$ .

$\frac{y - 4}{20} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Simplify terms.

Cancel the common factor of $4$ .

Factor $4$ out of $20$ .

$\frac{y - 4}{4 (5)} \cdot 8 = \frac{y + 2}{8} \cdot 8$

Factor $4$ out of $8$ .

$\frac{y - 4}{4 \cdot 5} \cdot (4 \cdot 2) = \frac{y + 2}{8} \cdot 8$

Cancel the common factor.

$\frac{y - 4}{4 \cdot 5} \cdot (4 \cdot 2) = \frac{y + 2}{8} \cdot 8$

Rewrite the expression.

$\frac{y - 4}{5} \cdot 2 = \frac{y + 2}{8} \cdot 8$

Combine $\frac{y - 4}{5}$ and $2$ .

$\frac{(y - 4) \cdot 2}{5} = \frac{y + 2}{8} \cdot 8$

Move $2$ to the left of $y - 4$ .

$\frac{2 (y - 4)}{5} = \frac{y + 2}{8} \cdot 8$

Simplify the right side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{2 (y - 4)}{5} = \frac{y + 2}{8} \cdot 8$

Rewrite the expression.

$\frac{2 (y - 4)}{5} = y + 2$

Step 3

Solve for $y$ .

Multiply both sides by $5$ .

$\frac{2 (y - 4)}{5} \cdot 5 = (y + 2) \cdot 5$

Simplify.

Simplify the left side.

Simplify $\frac{2 (y - 4)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (y - 4)}{5} \cdot 5 = (y + 2) \cdot 5$

Rewrite the expression.

$2 (y - 4) = (y + 2) \cdot 5$

Apply the distributive property.

$2 y + 2 \cdot - 4 = (y + 2) \cdot 5$

Multiply $2$ by $- 4$ .

$2 y - 8 = (y + 2) \cdot 5$

Simplify the right side.

Simplify $(y + 2) \cdot 5$ .

Apply the distributive property.

$2 y - 8 = y \cdot 5 + 2 \cdot 5$

Simplify the expression.

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

$2 y - 8 = 5 \cdot y + 2 \cdot 5$

Multiply $2$ by $5$ .

$2 y - 8 = 5 y + 10$

Solve for $y$ .

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

Subtract $5 y$ from both sides of the equation.

$2 y - 8 - 5 y = 10$

Subtract $5 y$ from $2 y$ .

$- 3 y - 8 = 10$

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

Add $8$ to both sides of the equation.

$- 3 y = 10 + 8$

Add $10$ and $8$ .

$- 3 y = 18$

Divide each term in $- 3 y = 18$ by $- 3$ and simplify.

Divide each term in $- 3 y = 18$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{18}{- 3}$

Divide $y$ by $1$ .

$y = \frac{18}{- 3}$

Simplify the right side.

Divide $18$ by $- 3$ .

$y = - 6$

Solve for y y/4-(y+1)/5=(y+2)/8

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