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

Answer:

The possible range of $\dfrac{8}{3}-5mx$ is:

                   (-9,-3) i.e. $-9<\dfrac{8}{3}-5mx<-3$

Step-by-step 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:

$\dfrac{9}{3}<\dfrac{15mx}{3}-\dfrac{8}{3}<\dfrac{27}{3}\\\\i.e.\\\\3<5mx-\dfrac{8}{3}<9$

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

i.e.

$-3>-(5mx-\dfrac{8}{3})>-9\\\\i.e.\\\\-3>\dfrac{8}{3}-5mx>-9$

i.e.

$-9<\dfrac{8}{3}-5mx<-3$

Hence, the possible range of $\dfrac{8}{3}-5mx$ is:

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