jjack0310 wrote:
Sorry. It is not clear.
Can you explain what was wrong with the way I was approaching the problem?
I mean other than the part that you marked red, what was I doing wrong? Do I have to solve theproblem using the solution that you mentioned?
If x > -2, how is |x + 2| = (x - 2)?
Is there an identity that I am missing?
If I plug in, X = -1, |x + 2| = 1, but (x - 2) = -3
Why the discrepancy? What identity am I missing?
There was a typo:
When \(x\leq{-2}\), then \(|x+2|=-(x+2)\)
When \(x>{-2}\), then \(|x+2|=(x+2)\).
Absolute value properties:When \(x
\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);
When \(x
\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).
For our question, when x>-2 (when x+2>0), |x+2|=x+2.
Hope it's clear.
Got it.
Final question, why are there two possibilities for when x = 0? Is that correct? or a typo?