Solve 4/7-4/3y=-2/3

$$\frac { 4 } { 7 } - \frac { 4 } { 3 } y = - \frac { 2 } { 3 }$$

Solve for y

$$y=\frac{13}{14}\approx 0.928571429$$

Steps for Solving Linear Equation

Subtract \frac{4}{7} from both sides.

$$-\frac{4}{3}y=-\frac{2}{3}-\frac{4}{7}$$

Least common multiple of 3 and 7 is 21. Convert -\frac{2}{3} and \frac{4}{7} to fractions with denominator 21.

$$-\frac{4}{3}y=-\frac{14}{21}-\frac{12}{21}$$

Since -\frac{14}{21} and \frac{12}{21} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{3}y=\frac{-14-12}{21}$$

Subtract 12 from -14 to get -26.

$$-\frac{4}{3}y=-\frac{26}{21}$$

Multiply both sides by -\frac{3}{4}, the reciprocal of -\frac{4}{3}.

$$y=-\frac{26}{21}\left(-\frac{3}{4}\right)$$

Multiply -\frac{26}{21} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-26\left(-3\right)}{21\times 4}$$

Do the multiplications in the fraction \frac{-26\left(-3\right)}{21\times 4}.

$$y=\frac{78}{84}$$

Reduce the fraction \frac{78}{84} to lowest terms by extracting and canceling out 6.

$$y=\frac{13}{14}$$