Solve 3y-4/3=-1/5y+6/5

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

Solve for y

$$y=\frac{19}{24}\approx 0.791666667$$

Steps for Solving Linear Equation

Add \frac{1}{5}y to both sides.

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

Combine 3y and \frac{1}{5}y to get \frac{16}{5}y.

$$\frac{16}{5}y-\frac{4}{3}=\frac{6}{5}$$

Add \frac{4}{3} to both sides.

$$\frac{16}{5}y=\frac{6}{5}+\frac{4}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{16}{5}y=\frac{18}{15}+\frac{20}{15}$$

Since \frac{18}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{16}{5}y=\frac{18+20}{15}$$

Add 18 and 20 to get 38.

$$\frac{16}{5}y=\frac{38}{15}$$

Multiply both sides by \frac{5}{16}, the reciprocal of \frac{16}{5}.

$$y=\frac{38}{15}\times \frac{5}{16}$$

Multiply \frac{38}{15} times \frac{5}{16} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{38\times 5}{15\times 16}$$

Do the multiplications in the fraction \frac{38\times 5}{15\times 16}.

$$y=\frac{190}{240}$$

Reduce the fraction \frac{190}{240} to lowest terms by extracting and canceling out 10.

$$y=\frac{19}{24}$$