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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Pls help 2 :How many roots does this equation have?
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Case 1: |x+2| - 2 = 2, implying that |x+2| = 4himu wrote:How many roots does the equation || x +2 | - 2 | = 2 have?
A. 0
B. 1
C. 2
D. 3
E. 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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
