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

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

Step 1

Multiply both sides by $5$ .

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

Step 2

Simplify.

Simplify the left side.

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

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

To write $- \frac{y + 1}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{8}{8}$ .

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

Multiply $5$ by $8$ .

$(\frac{8}{40} - \frac{y + 1}{8} \cdot \frac{5}{5}) \cdot 5 = \frac{y}{5} \cdot 5$

Multiply $\frac{y + 1}{8}$ by $\frac{5}{5}$ .

$(\frac{8}{40} - \frac{(y + 1) \cdot 5}{8 \cdot 5}) \cdot 5 = \frac{y}{5} \cdot 5$

Multiply $8$ by $5$ .

$(\frac{8}{40} - \frac{(y + 1) \cdot 5}{40}) \cdot 5 = \frac{y}{5} \cdot 5$

Combine the numerators over the common denominator.

$\frac{8 - (y + 1) \cdot 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Simplify the numerator.

Apply the distributive property.

$\frac{8 + (- y - 1 \cdot 1) \cdot 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Multiply $- 1$ by $1$ .

$\frac{8 + (- y - 1) \cdot 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Apply the distributive property.

$\frac{8 - y \cdot 5 - 1 \cdot 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Multiply $5$ by $- 1$ .

$\frac{8 - 5 y - 1 \cdot 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Multiply $- 1$ by $5$ .

$\frac{8 - 5 y - 5}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Subtract $5$ from $8$ .

$\frac{- 5 y + 3}{40} \cdot 5 = \frac{y}{5} \cdot 5$

Simplify terms.

Cancel the common factor of $5$ .

Factor $5$ out of $40$ .

$\frac{- 5 y + 3}{5 (8)} \cdot 5 = \frac{y}{5} \cdot 5$

Cancel the common factor.

$\frac{- 5 y + 3}{5 \cdot 8} \cdot 5 = \frac{y}{5} \cdot 5$

Rewrite the expression.

$\frac{- 5 y + 3}{8} = \frac{y}{5} \cdot 5$

Factor $- 1$ out of $- 5 y$ .

$\frac{- (5 y) + 3}{8} = \frac{y}{5} \cdot 5$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (5 y) - 1 (- 3)}{8} = \frac{y}{5} \cdot 5$

Factor $- 1$ out of $- (5 y) - 1 (- 3)$ .

$\frac{- (5 y - 3)}{8} = \frac{y}{5} \cdot 5$

Simplify the expression.

Rewrite $- (5 y - 3)$ as $- 1 (5 y - 3)$ .

$\frac{- 1 (5 y - 3)}{8} = \frac{y}{5} \cdot 5$

Move the negative in front of the fraction.

$- \frac{5 y - 3}{8} = \frac{y}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$- \frac{5 y - 3}{8} = \frac{y}{5} \cdot 5$

Rewrite the expression.

$- \frac{5 y - 3}{8} = y$

Step 3

Solve for $y$ .

Multiply both sides by $8$ .

$- \frac{5 y - 3}{8} \cdot 8 = y \cdot 8$

Simplify.

Simplify the left side.

Simplify $- \frac{5 y - 3}{8} \cdot 8$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{5 y - 3}{8}$ into the numerator.

$\frac{- (5 y - 3)}{8} \cdot 8 = y \cdot 8$

Cancel the common factor.

$\frac{- (5 y - 3)}{8} \cdot 8 = y \cdot 8$

Rewrite the expression.

$- (5 y - 3) = y \cdot 8$

Apply the distributive property.

$- (5 y) - - 3 = y \cdot 8$

Multiply.

Multiply $5$ by $- 1$ .

$- 5 y - - 3 = y \cdot 8$

Multiply $- 1$ by $- 3$ .

$- 5 y + 3 = y \cdot 8$

Simplify the right side.

Move $8$ to the left of $y$ .

$- 5 y + 3 = 8 y$

Solve for $y$ .

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

Subtract $8 y$ from both sides of the equation.

$- 5 y + 3 - 8 y = 0$

Subtract $8 y$ from $- 5 y$ .

$- 13 y + 3 = 0$

Subtract $3$ from both sides of the equation.

$- 13 y = - 3$

Divide each term in $- 13 y = - 3$ by $- 13$ and simplify.

Divide each term in $- 13 y = - 3$ by $- 13$ .

$\frac{- 13 y}{- 13} = \frac{- 3}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 y}{- 13} = \frac{- 3}{- 13}$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{3}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{13}$

Decimal Form:

$y = 0.\overline{230769}$

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

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