Question 9116
{{{2 <= 3-x <= 8}}}


First you must think of this as an inequality in three parts:  the left part, the middle part, and the right part.  If you have three children (or in my case, GRANDCHILDREN!) then if you do something for one of them, you had better be prepared to do it for ALL THREE!  The objective is to get the x by itself.  You have to undo everything that was done to the x, in reverse order.  


In this case, the x was multiplied by -1, and then 3 was added.  You need to UNDO these steps in reverse order, by first subtracting the 3 and secondly by dividing by -1.  Remember, if you subtract 3, you have to do it to the left, to the center, and to the right.


{{{2 <= 3-x <= 8}}}
{{{2 - 3 <= 3 - 3-x <= 8- 3}}}
{{{-1 <= -x <= 5}}}


Now, divide by -1:

{{{(-1)/-1 <= (-x)/-1 <= 5/-1}}}
{{{1 >= x >= -5 }}}

which means that x is between -5 and 1, including both endpoints.


R^2 at SCC


Next, divide all three parts by -1.