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Bunuel
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 21 Feb 2023, 04:03
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D
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Difficulty:

55% (hard)

Question Stats:

63% (01:31) correct 37% (01:33) wrong based on 423 sessions

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How many distinct solutions does the equation |1 - |x - 215|| = 1 have?

A. None

B. One

C. Two

D. Three

E. Four
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D
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Bunuel
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 24 Feb 2023, 01:58
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Can someone please explain why there are three solutions and not two?
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have?

A. None

B. One

C. Two

D. Three

E. Four

|1 - |x - 215|| = 1:

Case 1:
1 - |x - 215| = 1
|x - 215| = 0
x = 215.

Case 2:
1 - |x - 215| = -1
|x - 215| = 2
x - 215 = 2 or x - 215 = -2
x = 217 or x = 213.

So, x can be 213, 215, and 217.

Answer: D.

Hope it helps.
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 21 Feb 2023, 10:50
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|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
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BusinessAdmin
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 23 Feb 2023, 19:25
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Can someone please explain why there are three solutions and not two?
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How many distinct solutions does the equation |1 - |x - 215|| = 1 have Updated on: 10 Jan 2025, 06:31
Originally posted by BrushMyQuant on 10 Oct 2024, 22:39.
Last edited by BrushMyQuant on 10 Jan 2025, 06:31, edited 1 time in total.
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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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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 13 Oct 2024, 10:46
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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
Show more


213 is also a possibile solution

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How many distinct solutions does the equation |1 - |x - 215|| = 1 have 15 Dec 2025, 03:56
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