Solve 4/5(y+5/6)-2/3(y-1/4)=frac{7}{6}

$$\frac { 4 } { 5 } ( y + \frac { 5 } { 6 } ) - \frac { 2 } { 3 } ( y - \frac { 1 } { 4 } ) = \frac { 7 } { 6 }$$

Solve for y

$$y = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{5} by y+\frac{5}{6}.

$$\frac{4}{5}y+\frac{4}{5}\times \frac{5}{6}-\frac{2}{3}\left(y-\frac{1}{4}\right)=\frac{7}{6}$$

Multiply \frac{4}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}y+\frac{4\times 5}{5\times 6}-\frac{2}{3}\left(y-\frac{1}{4}\right)=\frac{7}{6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{5}y+\frac{4}{6}-\frac{2}{3}\left(y-\frac{1}{4}\right)=\frac{7}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}y+\frac{2}{3}-\frac{2}{3}\left(y-\frac{1}{4}\right)=\frac{7}{6}$$

Use the distributive property to multiply -\frac{2}{3} by y-\frac{1}{4}.

$$\frac{4}{5}y+\frac{2}{3}-\frac{2}{3}y-\frac{2}{3}\left(-\frac{1}{4}\right)=\frac{7}{6}$$

Multiply -\frac{2}{3} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}y+\frac{2}{3}-\frac{2}{3}y+\frac{-2\left(-1\right)}{3\times 4}=\frac{7}{6}$$

Do the multiplications in the fraction \frac{-2\left(-1\right)}{3\times 4}.

$$\frac{4}{5}y+\frac{2}{3}-\frac{2}{3}y+\frac{2}{12}=\frac{7}{6}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}y+\frac{2}{3}-\frac{2}{3}y+\frac{1}{6}=\frac{7}{6}$$

Combine \frac{4}{5}y and -\frac{2}{3}y to get \frac{2}{15}y.

$$\frac{2}{15}y+\frac{2}{3}+\frac{1}{6}=\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{2}{15}y+\frac{4}{6}+\frac{1}{6}=\frac{7}{6}$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{2}{15}y+\frac{4+1}{6}=\frac{7}{6}$$

Add 4 and 1 to get 5.

$$\frac{2}{15}y+\frac{5}{6}=\frac{7}{6}$$

Subtract \frac{5}{6} from both sides.

$$\frac{2}{15}y=\frac{7}{6}-\frac{5}{6}$$

Since \frac{7}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{15}y=\frac{7-5}{6}$$

Subtract 5 from 7 to get 2.

$$\frac{2}{15}y=\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{15}y=\frac{1}{3}$$

Multiply both sides by \frac{15}{2}, the reciprocal of \frac{2}{15}.

$$y=\frac{1}{3}\times \frac{15}{2}$$

Multiply \frac{1}{3} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{1\times 15}{3\times 2}$$

Do the multiplications in the fraction \frac{1\times 15}{3\times 2}.

$$y=\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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