Question

If 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?

Answer 1

9<15mx-8<27
Divide the all by 3
3<5mx-8/3<9
After that times all by -1
-3<8/3-5mx<-9

Answer 2

The possible range of
`(8)/(3)-5mx` is:

(-9,-3) i.e.
`-9<(8)/(3)-5mx<-3`

Explanation:

We are given a set of inequalities of the form:

`9<15mx-8<27`

Now when we divide all of the inequality by 3 we get that:

`(9)/(3)<(15mx)/(3)-(8)/(3)<(27)/(3)\\\\i.e.\\\\3<5mx-(8)/(3)<9`

Now when we multiply the inequality by -1 then the sign of the inequality gets interchanged.

i.e.

`-3>-(5mx-(8)/(3))>-9\\\\i.e.\\\\-3>(8)/(3)-5mx>-9`

i.e.

`-9<(8)/(3)-5mx<-3`

Hence, the possible range of
`(8)/(3)-5mx` is:

(-9,-3) i.e. between -9 and -3 with -9 and -3 excluded from the range.