Solve 5/6y+1=-1/3y+5/9

$$\frac { 5 } { 6 } y + 1 = - \frac { 1 } { 3 } y + \frac { 5 } { 9 }$$

Solve for y

$$y=-\frac{8}{21}\approx -0.380952381$$

Steps for Solving Linear Equation

Add \frac{1}{3}y to both sides.

$$\frac{5}{6}y+1+\frac{1}{3}y=\frac{5}{9}$$

Combine \frac{5}{6}y and \frac{1}{3}y to get \frac{7}{6}y.

$$\frac{7}{6}y+1=\frac{5}{9}$$

Subtract 1 from both sides.

$$\frac{7}{6}y=\frac{5}{9}-1$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{7}{6}y=\frac{5}{9}-\frac{9}{9}$$

Since \frac{5}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}y=\frac{5-9}{9}$$

Subtract 9 from 5 to get -4.

$$\frac{7}{6}y=-\frac{4}{9}$$

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}.

$$y=-\frac{4}{9}\times \frac{6}{7}$$

Multiply -\frac{4}{9} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-4\times 6}{9\times 7}$$

Do the multiplications in the fraction \frac{-4\times 6}{9\times 7}.

$$y=\frac{-24}{63}$$

Reduce the fraction \frac{-24}{63} to lowest terms by extracting and canceling out 3.

$$y=-\frac{8}{21}$$