Solve -3/5+2/3=-5/4y+2/5y

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

Solve for y

$$y=-\frac{4}{51}\approx -0.078431373$$

Steps for Solving Linear Equation

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

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

Least common multiple of 5 and 3 is 15. Convert -\frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$-\frac{9}{15}+\frac{10}{15}=-\frac{5}{4}y+\frac{2}{5}y$$

Since -\frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{-9+10}{15}=-\frac{5}{4}y+\frac{2}{5}y$$

Add -9 and 10 to get 1.

$$\frac{1}{15}=-\frac{5}{4}y+\frac{2}{5}y$$

Combine -\frac{5}{4}y and \frac{2}{5}y to get -\frac{17}{20}y.

$$\frac{1}{15}=-\frac{17}{20}y$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{17}{20}y=\frac{1}{15}$$

Multiply both sides by -\frac{20}{17}, the reciprocal of -\frac{17}{20}.

$$y=\frac{1}{15}\left(-\frac{20}{17}\right)$$

Multiply \frac{1}{15} times -\frac{20}{17} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{1\left(-20\right)}{15\times 17}$$

Do the multiplications in the fraction \frac{1\left(-20\right)}{15\times 17}.

$$y=\frac{-20}{255}$$

Reduce the fraction \frac{-20}{255} to lowest terms by extracting and canceling out 5.

$$y=-\frac{4}{51}$$