Absolute Value inequalities: |x + 2| - x >= 0

G

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1) In this problem:

. . .|x+2| - x > 0

the answer is:

. . .{x | x is an element of R (the real numbers)}

Why? Also, why, on the number line, there is just one arrow with both ends point opposite.

2) Also this:

. . .|2x| > -64

there is the same answer and I have the same question

thanks a ton
smile.gif
 
Well, what answer did you get? What steps did you take to get that answer? (Or are you requesting links to lessons, because you're not familiar with the topic...?)

Thank you.

Eliz.
 
These are "think" problems. You should not be struggling with these.

The second, |2x| ≥ -64, is trivial. Absolute values are nonnegative, always.

The first, |x+2| - x ≥ 0, is just a little tricker. With a small modification:

|x+2| ≥ x

It is now quite obvious. If x < 0, see the problem above. If x > 0, well, that's pretty obvious, too.
 
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