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

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

Solve for y

$$y = \frac{30}{7} = 4\frac{2}{7} \approx 4.285714286$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{2y}{3} times \frac{5}{5}. Multiply \frac{3y}{5} times \frac{3}{3}.

$$\frac{5\times 2y}{15}-\frac{3\times 3y}{15}+4=y$$

Since \frac{5\times 2y}{15} and \frac{3\times 3y}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 2y-3\times 3y}{15}+4=y$$

Do the multiplications in 5\times 2y-3\times 3y.

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

Combine like terms in 10y-9y.

$$\frac{y}{15}+4=y$$

Subtract y from both sides.

$$\frac{y}{15}+4-y=0$$

Combine \frac{y}{15} and -y to get -\frac{14}{15}y.

$$-\frac{14}{15}y+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{14}{15}y=-4$$

Multiply both sides by -\frac{15}{14}, the reciprocal of -\frac{14}{15}.

$$y=-4\left(-\frac{15}{14}\right)$$

Express -4\left(-\frac{15}{14}\right) as a single fraction.

$$y=\frac{-4\left(-15\right)}{14}$$

Multiply -4 and -15 to get 60.

$$y=\frac{60}{14}$$

Reduce the fraction \frac{60}{14} to lowest terms by extracting and canceling out 2.

$$y=\frac{30}{7}$$