(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the solution set of:

[tex]|x+1| + |x-2| \leq 5 [/tex]

2. Relevant equations

I'm going to rearrange this to

[tex]|x+1| \leq 5 - |x-2|[/tex]

3. 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

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# Solving Modulus inequalities

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