mathematics

Question

Solve the compound inequality

 

-3x <-12 and x-3 <8

Answer 1

We want to isolate x on one side of each equality:

 

-3x < -12 

3x > 12        [multiply both sides by (-1) reverses the sense of the inequality]

x > 4           [dividing both sides by (+3) retains the sense of the inequality]

 

x-3 < 8

x < 11          [adding (+3) to both sides retains the sense of the inequality]

 

So,

    -3x<-12   and   x-3<8

       x>4      and   x<11

              4 < x < 11                [combing the "and"; note x<4 is 4<x]