Solve 5/6y-3/8(20-y)=7

$$\frac { 5 } { 6 } y - \frac { 3 } { 8 } ( 20 - y ) = 7$$

Solve for y

$$y=12$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{3}{8} by 20-y.

$$\frac{5}{6}y-\frac{3}{8}\times 20-\frac{3}{8}\left(-1\right)y=7$$

Express -\frac{3}{8}\times 20 as a single fraction.

$$\frac{5}{6}y+\frac{-3\times 20}{8}-\frac{3}{8}\left(-1\right)y=7$$

Multiply -3 and 20 to get -60.

$$\frac{5}{6}y+\frac{-60}{8}-\frac{3}{8}\left(-1\right)y=7$$

Reduce the fraction \frac{-60}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{6}y-\frac{15}{2}-\frac{3}{8}\left(-1\right)y=7$$

Multiply -\frac{3}{8} and -1 to get \frac{3}{8}.

$$\frac{5}{6}y-\frac{15}{2}+\frac{3}{8}y=7$$

Combine \frac{5}{6}y and \frac{3}{8}y to get \frac{29}{24}y.

$$\frac{29}{24}y-\frac{15}{2}=7$$

Add \frac{15}{2} to both sides.

$$\frac{29}{24}y=7+\frac{15}{2}$$

Convert 7 to fraction \frac{14}{2}.

$$\frac{29}{24}y=\frac{14}{2}+\frac{15}{2}$$

Since \frac{14}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{29}{24}y=\frac{14+15}{2}$$

Add 14 and 15 to get 29.

$$\frac{29}{24}y=\frac{29}{2}$$

Multiply both sides by \frac{24}{29}, the reciprocal of \frac{29}{24}.

$$y=\frac{29}{2}\times \frac{24}{29}$$

Multiply \frac{29}{2} times \frac{24}{29} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{29\times 24}{2\times 29}$$

Cancel out 29 in both numerator and denominator.

$$y=\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$y=12$$