Hi All,
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 equation 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:
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Rich
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