Solve 1/2(4y+2)-20<-1/3(9y-3)

$$\frac { 1 } { 2 } ( 4 y + 2 ) - 20 < - \frac { 1 } { 3 } ( 9 y - 3 )$$

Solve for y

$$y<4$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 4y+2.

$$\frac{1}{2}\times 4y+\frac{1}{2}\times 2-20<-\frac{1}{3}\left(9y-3\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}y+\frac{1}{2}\times 2-20<-\frac{1}{3}\left(9y-3\right)$$

Divide 4 by 2 to get 2.

$$2y+\frac{1}{2}\times 2-20<-\frac{1}{3}\left(9y-3\right)$$

Cancel out 2 and 2.

$$2y+1-20<-\frac{1}{3}\left(9y-3\right)$$

Subtract 20 from 1 to get -19.

$$2y-19<-\frac{1}{3}\left(9y-3\right)$$

Use the distributive property to multiply -\frac{1}{3} by 9y-3.

$$2y-19<-\frac{1}{3}\times 9y-\frac{1}{3}\left(-3\right)$$

Express -\frac{1}{3}\times 9 as a single fraction.

$$2y-19<\frac{-9}{3}y-\frac{1}{3}\left(-3\right)$$

Divide -9 by 3 to get -3.

$$2y-19<-3y-\frac{1}{3}\left(-3\right)$$

Express -\frac{1}{3}\left(-3\right) as a single fraction.

$$2y-19<-3y+\frac{-\left(-3\right)}{3}$$

Multiply -1 and -3 to get 3.

$$2y-19<-3y+\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$2y-19<-3y+1$$

Add 3y to both sides.

$$2y-19+3y<1$$

Combine 2y and 3y to get 5y.

$$5y-19<1$$

Add 19 to both sides.

$$5y<1+19$$

Add 1 and 19 to get 20.

$$5y<20$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$y<\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$y<4$$