Solve 1/5(y-3)=1/6(y+4)

$$\frac { 1 } { 5 } ( y - 3 ) = \frac { 1 } { 6 } ( y + 4 )$$

Solve for y

$$y=38$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by y-3.

$$\frac{1}{5}y+\frac{1}{5}\left(-3\right)=\frac{1}{6}\left(y+4\right)$$

Multiply \frac{1}{5} and -3 to get \frac{-3}{5}.

$$\frac{1}{5}y+\frac{-3}{5}=\frac{1}{6}\left(y+4\right)$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{1}{5}y-\frac{3}{5}=\frac{1}{6}\left(y+4\right)$$

Use the distributive property to multiply \frac{1}{6} by y+4.

$$\frac{1}{5}y-\frac{3}{5}=\frac{1}{6}y+\frac{1}{6}\times 4$$

Multiply \frac{1}{6} and 4 to get \frac{4}{6}.

$$\frac{1}{5}y-\frac{3}{5}=\frac{1}{6}y+\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}y-\frac{3}{5}=\frac{1}{6}y+\frac{2}{3}$$

Subtract \frac{1}{6}y from both sides.

$$\frac{1}{5}y-\frac{3}{5}-\frac{1}{6}y=\frac{2}{3}$$

Combine \frac{1}{5}y and -\frac{1}{6}y to get \frac{1}{30}y.

$$\frac{1}{30}y-\frac{3}{5}=\frac{2}{3}$$

Add \frac{3}{5} to both sides.

$$\frac{1}{30}y=\frac{2}{3}+\frac{3}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{1}{30}y=\frac{10}{15}+\frac{9}{15}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{30}y=\frac{10+9}{15}$$

Add 10 and 9 to get 19.

$$\frac{1}{30}y=\frac{19}{15}$$

Multiply both sides by 30, the reciprocal of \frac{1}{30}.

$$y=\frac{19}{15}\times 30$$

Express \frac{19}{15}\times 30 as a single fraction.

$$y=\frac{19\times 30}{15}$$

Multiply 19 and 30 to get 570.

$$y=\frac{570}{15}$$

Divide 570 by 15 to get 38.

$$y=38$$