SOLUTION: Please help me solve this inequelitie: |x-2| + |x+3|

SOLUTION: Please help me solve this inequelitie: |x-2| + |x+3| < |2x-2|

Question 735156: Please help me solve this inequelitie: |x-2| + |x+3| < |2x-2|
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This can have eight different equations taking account of the possibility of each absolute value being either greater-than-or-equal-to-zero OR less-than-zero. Setting up a tree diagram on this web system is inconvenient, maybe very unappealing. Here is a try at representing the possiblilities:

Each Expression: _________x-2____________x+3____________2x-2
------------------------------------------------------------------------------
If greater or equalzero ____x-2___________x+3____________2x-2
OR
If less than zero________2-x____________-x-3____________2-2x
------------------------------------------------------------------------------

Those are the possibilities. Building a set of tree diagrams for ALL of them starts like this: for x-2, may have x+3 or -x-3; for x-2 and x+3, may have 2x-2 or 2-2x.

...and on and on like that until you have all eight sets of expressions. Right now I'm not patient/clever enough to represent this any better in plain text. Maybe my method is also inefficient. A real tree diagram set would make this much easier to see.

My found eight inequalities are:
x-2+x+3<2x-2
.
x-2+x+3<2-2x
.
x-2-x-3<2x-2
.
x-2-x-3<2-2x
.
2-x+x+3<2x-2
.
2-x+x+3<2-2x
.
2-x-x-3<2x-2
.
2-x-x-3<2-2x

Solve each of those eight individually, and maybe check the results of each of their results.
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