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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
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If greater or equalzero ____x-2___________x+3____________2x-2
OR
If less than zero________2-x____________-x-3____________2-2x
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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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