Given the inequality:
[tex]-33<-7n-12<-26[/tex]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:
[tex]\begin{gathered} (-33<-7n-12<-26)+12 \\ \Rightarrow-33+12<-7n-12+12<-26+12 \\ \Rightarrow-21<-7n<-14 \end{gathered}[/tex]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:
[tex]\begin{gathered} (-21<-7n<-14)\frac{1}{-7} \\ \Rightarrow-\frac{21}{-7}>-\frac{7n}{7}>-\frac{14}{-7} \\ \Rightarrow3>n>2 \end{gathered}[/tex]therefore, the solution is (2,3) and it looks like this in the number line:
