I don't know how to solve a conjucnction -2 < a + 3 < 8 and graph the solution.
Thank you for your help.
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 < a + 3 < 8
Add -3 to ALL THREE SIDES:
-2 < a + 3 < 8
-3 -3 -3
覧覧覧覧覧覧覧覧
-5 < a < 5
So the solution is -5 < a < 5
Graphed on a number line it looks like this:
-------n============================o------
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
There is a closed circle "n"at -5 and an open circle "o"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
"<" 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
[-5, 5)
Edwin
