Question 10944
Think of this (it's a DOUBLE inequality) as an inequality in three parts.  
For example, if you had a<b<c, it's like you have three children (or grandchildren) in the family:  a is for Alice, b is for Betty, and c is for Carol.  Alice is younger than Betty, and Betty is younger than Carol.  Therefore, without saying, Alice must be younger than Carol.


Now if you have three children in the family, if you do something for one, you need to do it for ALL three.  In the case of 3<2x+11<17 , you are saying that 3 is the smallest (youngest), 17 is the largest (oldest), and the 2x+11 represents something in between.


The name of the game with 3<2x+11<17 is to get the x by itself in the middle.  In order to do this, you must eliminate the 11 with a negative 11, and undo the 2 which is multiplied times x by DIVIDING by 2.  However, whatever you do, you must do to EACH of the three parts:


Subtract 11 from each part:
3<2x+11<17 
3-11 <2x+11-11<17 -11 


-8< 2x < 6


Now to undo the 2, divide each of the three parts by 2:

{{{ (-8)/2 < (2x)/2 < 6/2 }}}

{{{ -4 < x < 3}}}


This means in words that x must be between -4 and 3.  


R^2 at SCC