Evaluate 2/3(y+2)-5/6(y-1)=5/4(y-3)-4

$\frac{2}{3} (y + 2) - \frac{5}{6} (y - 1) = \frac{5}{4} (y - 3) - 4$

Simplify $\frac{2}{3} \cdot (y + 2) - \frac{5}{6} \cdot (y - 1)$ .

Simplify each term.

Apply the distributive property.

$\frac{2}{3} y + \frac{2}{3} \cdot 2 - \frac{5}{6} \cdot (y - 1) = \frac{5}{4} \cdot (y - 3) - 4$

Combine $\frac{2}{3}$ and $y$ .

$\frac{2 y}{3} + \frac{2}{3} \cdot 2 - \frac{5}{6} \cdot (y - 1) = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $\frac{2}{3} \cdot 2$ .

Combine $\frac{2}{3}$ and $2$ .

$\frac{2 y}{3} + \frac{2 \cdot 2}{3} - \frac{5}{6} \cdot (y - 1) = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $2$ by $2$ .

$\frac{2 y}{3} + \frac{4}{3} - \frac{5}{6} \cdot (y - 1) = \frac{5}{4} \cdot (y - 3) - 4$

Apply the distributive property.

$\frac{2 y}{3} + \frac{4}{3} - \frac{5}{6} y - \frac{5}{6} \cdot - 1 = \frac{5}{4} \cdot (y - 3) - 4$

Combine $y$ and $\frac{5}{6}$ .

$\frac{2 y}{3} + \frac{4}{3} - \frac{y \cdot 5}{6} - \frac{5}{6} \cdot - 1 = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $- \frac{5}{6} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$\frac{2 y}{3} + \frac{4}{3} - \frac{y \cdot 5}{6} + 1 (\frac{5}{6}) = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $\frac{5}{6}$ by $1$ .

$\frac{2 y}{3} + \frac{4}{3} - \frac{y \cdot 5}{6} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

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

$\frac{2 y}{3} + \frac{4}{3} - \frac{5 y}{6} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

To write $\frac{2 y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 y}{3} \cdot \frac{2}{2} - \frac{5 y}{6} + \frac{4}{3} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 y}{3}$ by $\frac{2}{2}$ .

$\frac{2 y \cdot 2}{3 \cdot 2} - \frac{5 y}{6} + \frac{4}{3} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $3$ by $2$ .

$\frac{2 y \cdot 2}{6} - \frac{5 y}{6} + \frac{4}{3} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 - 5 y}{6} + \frac{4}{3} + \frac{5}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 - 5 y + 5}{6} + \frac{4}{3} = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $2$ by $2$ .

$\frac{4 y - 5 y + 5}{6} + \frac{4}{3} = \frac{5}{4} \cdot (y - 3) - 4$

Subtract $5 y$ from $4 y$ .

$\frac{- y + 5}{6} + \frac{4}{3} = \frac{5}{4} \cdot (y - 3) - 4$

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- y + 5}{6} + \frac{4}{3} \cdot \frac{2}{2} = \frac{5}{4} \cdot (y - 3) - 4$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$\frac{- y + 5}{6} + \frac{4 \cdot 2}{3 \cdot 2} = \frac{5}{4} \cdot (y - 3) - 4$

Multiply $3$ by $2$ .

$\frac{- y + 5}{6} + \frac{4 \cdot 2}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Combine the numerators over the common denominator.

$\frac{- y + 5 + 4 \cdot 2}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{- y + 5 + 8}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Add $5$ and $8$ .

$\frac{- y + 13}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Simplify with factoring out.

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

$\frac{- (y) + 13}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Rewrite $13$ as $- 1 (- 13)$ .

$\frac{- (y) - 1 (- 13)}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Factor $- 1$ out of $- (y) - 1 (- 13)$ .

$\frac{- (y - 13)}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Simplify the expression.

Rewrite $- (y - 13)$ as $- 1 (y - 13)$ .

$\frac{- 1 (y - 13)}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Move the negative in front of the fraction.

$- \frac{y - 13}{6} = \frac{5}{4} \cdot (y - 3) - 4$

Simplify $\frac{5}{4} \cdot (y - 3) - 4$ .

Simplify each term.

Apply the distributive property.

$- \frac{y - 13}{6} = \frac{5}{4} y + \frac{5}{4} \cdot - 3 - 4$

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

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{5}{4} \cdot - 3 - 4$

Multiply $\frac{5}{4} \cdot - 3$ .

Combine $\frac{5}{4}$ and $- 3$ .

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{5 \cdot - 3}{4} - 4$

Multiply $5$ by $- 3$ .

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{- 15}{4} - 4$

Move the negative in front of the fraction.

$- \frac{y - 13}{6} = \frac{5 y}{4} - \frac{15}{4} - 4$

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

$- \frac{y - 13}{6} = \frac{5 y}{4} - \frac{15}{4} - 4 \cdot \frac{4}{4}$

Combine $- 4$ and $\frac{4}{4}$ .

$- \frac{y - 13}{6} = \frac{5 y}{4} - \frac{15}{4} + \frac{- 4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{- 15 - 4 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 4$ by $4$ .

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{- 15 - 16}{4}$

Subtract $16$ from $- 15$ .

$- \frac{y - 13}{6} = \frac{5 y}{4} + \frac{- 31}{4}$

Move the negative in front of the fraction.

$- \frac{y - 13}{6} = \frac{5 y}{4} - \frac{31}{4}$

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

Subtract $\frac{5 y}{4}$ from both sides of the equation.

$- \frac{y - 13}{6} - \frac{5 y}{4} = - \frac{31}{4}$

To write $- \frac{y - 13}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{y - 13}{6} \cdot \frac{2}{2} - \frac{5 y}{4} = - \frac{31}{4}$

To write $- \frac{5 y}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{y - 13}{6} \cdot \frac{2}{2} - \frac{5 y}{4} \cdot \frac{3}{3} = - \frac{31}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y - 13}{6}$ by $\frac{2}{2}$ .

$- \frac{(y - 13) \cdot 2}{6 \cdot 2} - \frac{5 y}{4} \cdot \frac{3}{3} = - \frac{31}{4}$

Multiply $6$ by $2$ .

$- \frac{(y - 13) \cdot 2}{12} - \frac{5 y}{4} \cdot \frac{3}{3} = - \frac{31}{4}$

Multiply $\frac{5 y}{4}$ by $\frac{3}{3}$ .

$- \frac{(y - 13) \cdot 2}{12} - \frac{5 y \cdot 3}{4 \cdot 3} = - \frac{31}{4}$

Multiply $4$ by $3$ .

$- \frac{(y - 13) \cdot 2}{12} - \frac{5 y \cdot 3}{12} = - \frac{31}{4}$

Combine the numerators over the common denominator.

$\frac{- (y - 13) \cdot 2 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Simplify the numerator.

Apply the distributive property.

$\frac{(- y - - 13) \cdot 2 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Multiply $- 1$ by $- 13$ .

$\frac{(- y + 13) \cdot 2 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Apply the distributive property.

$\frac{- y \cdot 2 + 13 \cdot 2 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Multiply $2$ by $- 1$ .

$\frac{- 2 y + 13 \cdot 2 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Multiply $13$ by $2$ .

$\frac{- 2 y + 26 - 5 y \cdot 3}{12} = - \frac{31}{4}$

Multiply $3$ by $- 5$ .

$\frac{- 2 y + 26 - 15 y}{12} = - \frac{31}{4}$

Subtract $15 y$ from $- 2 y$ .

$\frac{- 17 y + 26}{12} = - \frac{31}{4}$

Factor $- 1$ out of $- 17 y$ .

$\frac{- (17 y) + 26}{12} = - \frac{31}{4}$

Rewrite $26$ as $- 1 (- 26)$ .

$\frac{- (17 y) - 1 (- 26)}{12} = - \frac{31}{4}$

Factor $- 1$ out of $- (17 y) - 1 (- 26)$ .

$\frac{- (17 y - 26)}{12} = - \frac{31}{4}$

Rewrite $- (17 y - 26)$ as $- 1 (17 y - 26)$ .

$\frac{- 1 (17 y - 26)}{12} = - \frac{31}{4}$

Move the negative in front of the fraction.

$- \frac{17 y - 26}{12} = - \frac{31}{4}$

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

$- 12 (- \frac{17 y - 26}{12}) = - 12 (- \frac{31}{4})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 12 (- \frac{17 y - 26}{12})$ .

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{17 y - 26}{12}$ into the numerator.

$- 12 \frac{- (17 y - 26)}{12} = - 12 (- \frac{31}{4})$

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- (17 y - 26)}{12} = - 12 (- \frac{31}{4})$

Cancel the common factor.

$12 \cdot - 1 \frac{- (17 y - 26)}{12} = - 12 (- \frac{31}{4})$

Rewrite the expression.

$- - (17 y - 26) = - 12 (- \frac{31}{4})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (17 y - 26) = - 12 (- \frac{31}{4})$

Multiply $17 y - 26$ by $1$ .

$17 y - 26 = - 12 (- \frac{31}{4})$

Simplify the right side.

Simplify $- 12 (- \frac{31}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{31}{4}$ into the numerator.

$17 y - 26 = - 12 (\frac{- 31}{4})$

Factor $4$ out of $- 12$ .

$17 y - 26 = 4 (- 3) \frac{- 31}{4}$

Cancel the common factor.

$17 y - 26 = 4 \cdot - 3 \frac{- 31}{4}$

Rewrite the expression.

$17 y - 26 = - 3 \cdot - 31$

Multiply $- 3$ by $- 31$ .

$17 y - 26 = 93$

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

Add $26$ to both sides of the equation.

$17 y = 93 + 26$

Add $93$ and $26$ .

$17 y = 119$

Divide each term in $17 y = 119$ by $17$ and simplify.

Divide each term in $17 y = 119$ by $17$ .

$\frac{17 y}{17} = \frac{119}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{119}{17}$

Divide $y$ by $1$ .

$y = \frac{119}{17}$

Simplify the right side.

Divide $119$ by $17$ .

$y = 7$

Evaluate 2/3(y+2)-5/6(y-1)=5/4(y-3)-4

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