Question

How do you solve and graph `m-2< -8` or `m/8>1`?

Answer 1

`m<-6 or m>8` or in interval notation `m in (-oo,-6) uu (8,+oo)`

Explanation:

`m-2<-8 or m/8>1`

First consider: `m-2<-8`

Add 2 to both sides.

`-> m<-8+2`

`m<-6`

Next consider: `m/8>1`

Multiply both sides by 8.

`-> m>8`

Hence our compound inequality simplifies to: `m<-6 or m>8`
or in interval notation `m in (-oo,-6) uu (8,+oo)`

We can represent this graphically on a 2D plane where `m` is the horizontal axis, as below.

graph{(x+6)(-x+8)<0 [-14.24, 14.23, -7.12, 7.11]}

So, `m` may take all values on the horizontal axis in the shaded areas.