Solve 1/3(y+19)=3y-5(y-5)

$$\frac { 1 } { 3 } ( y + 19 ) = 3 y - 5 ( y - 5 )$$

Solve for y

$$y=8$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by y+19.

$$\frac{1}{3}y+\frac{1}{3}\times 19=3y-5\left(y-5\right)$$

Multiply \frac{1}{3} and 19 to get \frac{19}{3}.

$$\frac{1}{3}y+\frac{19}{3}=3y-5\left(y-5\right)$$

Use the distributive property to multiply -5 by y-5.

$$\frac{1}{3}y+\frac{19}{3}=3y-5y+25$$

Combine 3y and -5y to get -2y.

$$\frac{1}{3}y+\frac{19}{3}=-2y+25$$

Add 2y to both sides.

$$\frac{1}{3}y+\frac{19}{3}+2y=25$$

Combine \frac{1}{3}y and 2y to get \frac{7}{3}y.

$$\frac{7}{3}y+\frac{19}{3}=25$$

Subtract \frac{19}{3} from both sides.

$$\frac{7}{3}y=25-\frac{19}{3}$$

Convert 25 to fraction \frac{75}{3}.

$$\frac{7}{3}y=\frac{75}{3}-\frac{19}{3}$$

Since \frac{75}{3} and \frac{19}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{3}y=\frac{75-19}{3}$$

Subtract 19 from 75 to get 56.

$$\frac{7}{3}y=\frac{56}{3}$$

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$y=\frac{56}{3}\times \frac{3}{7}$$

Multiply \frac{56}{3} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{56\times 3}{3\times 7}$$

Cancel out 3 in both numerator and denominator.

$$y=\frac{56}{7}$$

Divide 56 by 7 to get 8.

$$y=8$$