Answer:
(a)
S={m∈ real numbers| [tex]m<\dfrac{-38}{3}[/tex]}
(b)
S=[tex](-\infty,\dfrac{-38}{3})[/tex]
Step-by-step explanation:
The inequality  is given as:
[tex]\dfrac{1}{2}\times(m+4)<\dfrac{1}{5}\times(m-9)[/tex]
Now on solving this inequality we have:
firstly we multiply both side by 10 and then combine the like terms in order to obtain our inequality:
[tex]5(m+4)<2(m-9)\\\\5m+20<2m-18\\\\5m-2m<-18-20\\\\3m<-38\\\\m<\dfrac{-38}{3}[/tex]
Hence, the solution set of the following inequality is the set of all those real numbers such that [tex]m<\dfrac{-38}{3}[/tex]
(a)
The solution set(S) in the set-builder notation could be represented as:
S={m∈ real numbers| [tex]m<\dfrac{-38}{3}[/tex]}
(b)
In interval notation we can write our solution set as:
S=[tex](-\infty,\dfrac{-38}{3})[/tex]
(c)
The graph of the solution set is attached to the answer.
