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Can someone please explain why there are three solutions and not two?
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧



We need to find how many distinct solutions does the equation |1 - |x - 215|| = 1 have?

Now, | 1 - Something | = 1
=> Something = 0 or 2
Making 1 - Something = 1 or -1 and | 1 - Something | = 1
=> | x - 215| = 0 or 2

We have two cases
-Case 1: | x - 215| = 0
=> x - 215 = 0
=> x = 215
-Case 2: | x - 215 | = 2
=> x - 215 = 2 or x - 215 = -2
=> x = 217 or 213

So, there are three solutions x = 213, 215, 217

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Absolute Values

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Rabab36
|1 - |x - 215|| = 1
solving we get 4 values of x

only 2 values of x satisfy equation
x=215 and x=217

thereofre option c correct


213 is also a possibile solution

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