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

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

Solve for y

$$y = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Steps for Solving Linear Equation

Cancel out \frac{2}{3} on both sides.

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

Divide 5 by 5 to get 1.

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

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

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

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

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

Subtract \frac{1}{2}y from both sides.

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

Combine 1y and -\frac{1}{2}y to get \frac{1}{2}y.

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

Subtract \frac{1}{2} from both sides.

$$\frac{1}{2}y=-\frac{3}{5}-\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{1}{2}y=-\frac{6}{10}-\frac{5}{10}$$

Since -\frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}y=\frac{-6-5}{10}$$

Subtract 5 from -6 to get -11.

$$\frac{1}{2}y=-\frac{11}{10}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$y=-\frac{11}{10}\times 2$$

Express -\frac{11}{10}\times 2 as a single fraction.

$$y=\frac{-11\times 2}{10}$$

Multiply -11 and 2 to get -22.

$$y=\frac{-22}{10}$$

Reduce the fraction \frac{-22}{10} to lowest terms by extracting and canceling out 2.

$$y=-\frac{11}{5}$$