- #1
thomas49th
- 655
- 0
Homework Statement
Find the solution set of:
[tex]|x+1| + |x-2| \leq 5 [/tex]
Homework Equations
I'm going to rearrange this to
[tex]|x+1| \leq 5 - |x-2|[/tex]
The Attempt at a Solution
Well i sketched a graph of it. The line 5-|x-2| cross the y-axis at 3 and it 'pongs' back of the x-axis at -3 (is there a proper name for this value of x). The line |x+1| at cross y at 1 and x at -1.
The graph lines seem to cross between -3 and -1. One of them is a pongy line (reflected up from the x-axis due to the modulus symbol) and the other is the original line.
5 - |x-2| = -|x+1|
|x-2| -5 = |x+1|
but how do i solve for that?
another concern i have is whether or the lines are going to cross again higher up (if you see what i mean). Is there a sound way of checking it.
Thanks