Question

Solve the inequality and write the solution set. Then graph the solution set. a. Write the solution set using​ set-builder notation. b. Write the solution set using interval notation. c. Graph the solution set. one half ​(mplus4​)less thanone fifth ​(mminus9​)

Answer 1

(a)

S={m∈ real numbers|
`m<(-38)/(3)`}

(b)

S=
`(-\infty,(-38)/(3))`

Explanation:

The inequality is given as:

`(1)/(2)*(m+4)<(1)/(5)*(m-9)`

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:

`5(m+4)<2(m-9)\\\\5m+20<2m-18\\\\5m-2m<-18-20\\\\3m<-38\\\\m<(-38)/(3)`

Hence, the solution set of the following inequality is the set of all those real numbers such that
`m<(-38)/(3)`

(a)

The solution set(S) in the set-builder notation could be represented as:

S={m∈ real numbers|
`m<(-38)/(3)`}

(b)

In interval notation we can write our solution set as:

S=
`(-\infty,(-38)/(3))`

(c)

The graph of the solution set is attached to the answer.