Solve 2/7y+5/6=-2/3y-5/6

$$\frac{ 2 }{ 7 } y+ \frac{ 5 }{ 6 } = - \frac{ 2 }{ 3 } y- \frac{ 5 }{ 6 }$$

Solve for y

$$y = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

Steps for Solving Linear Equation

Add \frac{2}{3}y to both sides.

$$\frac{2}{7}y+\frac{5}{6}+\frac{2}{3}y=-\frac{5}{6}$$

Combine \frac{2}{7}y and \frac{2}{3}y to get \frac{20}{21}y.

$$\frac{20}{21}y+\frac{5}{6}=-\frac{5}{6}$$

Subtract \frac{5}{6} from both sides.

$$\frac{20}{21}y=-\frac{5}{6}-\frac{5}{6}$$

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

$$\frac{20}{21}y=\frac{-5-5}{6}$$

Subtract 5 from -5 to get -10.

$$\frac{20}{21}y=\frac{-10}{6}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{20}{21}y=-\frac{5}{3}$$

Multiply both sides by \frac{21}{20}, the reciprocal of \frac{20}{21}.

$$y=-\frac{5}{3}\times \frac{21}{20}$$

Multiply -\frac{5}{3} times \frac{21}{20} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-5\times 21}{3\times 20}$$

Do the multiplications in the fraction \frac{-5\times 21}{3\times 20}.

$$y=\frac{-105}{60}$$

Reduce the fraction \frac{-105}{60} to lowest terms by extracting and canceling out 15.

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