Question 116226
I don't know how to solve a conjucnction -2 <u><</u> a + 3 < 8 and graph the solution. 

Thank you for your help. 
<pre><font size = 3><b>
The idea is to get the unknown alone in the middle for adding the same thing
to ALL THREE sides, and sometimes multiplying ALL THREE SIDES by the same
quantity. 

                                -2 <u><</u> a + 3 < 8

Add -3 to ALL THREE SIDES:

                                -2 <u><</u> a + 3 < 8
                                -3      -3  -3
                               覧覧覧覧覧覧覧覧 
                                -5 <u><</u> a     < 5

So the solution is -5 <u><</u> a < 5

Graphed on a number line it looks like this:
-------<font face = "webdings">n</font>============================<font size = 6>o</font>------
-7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7 
  
There is a closed circle "<font face = "webdings">n</font>"at -5 and an open circle "<font size = 6>o</font>"at +5.
The reason is because -5 is included with the shaded part,
but +5 is excluded.  That's because the -5 had the symbol
"<u><</u>" next to it whereas the +5 had the symbol "<" next
to it.  

Interval notation is an abbreviation for the graph above, where
a bracket denotes a closed circle and a parenthesis denotes an
open circle, and the endpoints of the shaded interval are in
between separated by a comma.  The above graph would be 
abbreviated with interval notation as

<font size = 5> [-5, 5) </font>

Edwin</pre><font>