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Pls help 2 :How many roots does this equation have?

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by himu » Mon Sep 08, 2014 1:27 am
got this one !

|x+2|-2 = + - 2

1. |x+2|-2=2 -->|x+2|=4, again, x+2=+ -4
1.1, x+2=4, x=2
1.2, x+2=-4, x=-6

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

So, x=-6,-2,2
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by GMATGuruNY » Mon Sep 08, 2014 2:55 am
himu wrote:How many roots does the equation || x +2 | - 2 | = 2 have?

A. 0
B. 1
C. 2
D. 3
E. 4
Case 1: |x+2| - 2 = 2, implying that |x+2| = 4
If x+2 = 4, then x=2.
If x+2 = -4, then x=-6.
For Case 1, there are two solutions: x=2 and x=-6.

Case 2: |x+2| - 2 = -2, implying that |x+2| = 0
For Case 2, there is only one solution: x=-2.

Total solutions:
x=-6, x=-2, x=2.

The correct answer is D.
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by [email protected] » Mon Sep 08, 2014 11:36 am
Hi himu,

Since this equation has an absolute value embedded inside another absolute value, the key to solving it is to work from the "outside" in...

We're given || X +2 | - 2 | = 2

Let's rewrite this as...

||something| - 2| = 2

Taking the "-2" and the "outside" absolute value into account, we need the left "side" of the calculation to equal EITHER 2 or -2....

So....

|something| - 2 = 2
|something| - 2 = -2

In the first option, we need |something| to equal 4
In the second option, we need |something| to equal 0

Now we can deal with the inner absolute value....

|X + 2| = 4

This has two solutions: -6 and +2

|X + 2| = 0

This has one solution: -2

Thus, we have 3 solutions/roots.

Final Answer: D

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