Question

9. Solve and graph the inequality below. -33 <-7n - 12 < -26

Answer 1

Given the inequality:

`-33<-7n-12<-26`

To find the solution set, the goal is to get the n alone between the inequality signs. First we have to get rid of the -12. For this, we can add 12 on both sides of the inequality to get the following:

`\begin{gathered} (-33<-7n-12<-26)+12 \\ \Rightarrow-33+12<-7n-12+12<-26+12 \\ \Rightarrow-21<-7n<-14 \end{gathered}`

Notice that -7 is multiplying n. To get rid of it, we have to divide by -7 the whole expression and since we are doing this with a negative number, then the inequality signs are going to change:

`\begin{gathered} (-21<-7n<-14)(1)/(-7) \\ \Rightarrow-(21)/(-7)>-(7n)/(7)>-(14)/(-7) \\ \Rightarrow3>n>2 \end{gathered}`

therefore, the solution is (2,3) and it looks like this in the number line: