Solve 3(r-6)+2<4(r+2)-21

$$3 ( r - 6 ) + 2 < 4 ( r + 2 ) - 21$$

Solve for r

$$r>-3$$

Solution Steps

Use the distributive property to multiply 3 by r-6.

$$3r-18+2<4\left(r+2\right)-21$$

Add -18 and 2 to get -16.

$$3r-16<4\left(r+2\right)-21$$

Use the distributive property to multiply 4 by r+2.

$$3r-16<4r+8-21$$

Subtract 21 from 8 to get -13.

$$3r-16<4r-13$$

Subtract 4r from both sides.

$$3r-16-4r<-13$$

Combine 3r and -4r to get -r.

$$-r-16<-13$$

Add 16 to both sides.

$$-r<-13+16$$

Add -13 and 16 to get 3.

$$-r<3$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$r>-3$$