Solve 7m+2<32+5(5m-8)-20m

$$7 m + 2 < 32 + 5 ( 5 m - 8 ) - 20 m$$

Solve for m

$$m<-5$$

Solution Steps

Use the distributive property to multiply 5 by 5m-8.

$$7m+2<32+25m-40-20m$$

Subtract 40 from 32 to get -8.

$$7m+2<-8+25m-20m$$

Combine 25m and -20m to get 5m.

$$7m+2<-8+5m$$

Subtract 5m from both sides.

$$7m+2-5m<-8$$

Combine 7m and -5m to get 2m.

$$2m+2<-8$$

Subtract 2 from both sides.

$$2m<-8-2$$

Subtract 2 from -8 to get -10.

$$2m<-10$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$m<\frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$m<-5$$