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anirchat
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If |x - 2| < 5, which of the following must be true? 16 Feb 2025, 05:00
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Please re-check the option in D. It says 0<x<3. Krunaal
Correct me if I am mistaken.
Krunaal
anirchat
I think the answer should be D under all circumstances.
If x = -1, then |x-2| < 5 => |-3| < 5 = 3 < 5 which is true. Thus, D. cannot be true under all circumstances.
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If |x - 2| < 5, which of the following must be true? 16 Feb 2025, 08:09
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anirchat
Please re-check the option in D. It says 0<x<3. Krunaal
Correct me if I am mistaken.
Krunaal
anirchat
I think the answer should be D under all circumstances.
If x = -1, then |x-2| < 5 => |-3| < 5 = 3 < 5 which is true. Thus, D. cannot be true under all circumstances.
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x can be -1, so it’s not necessary for x to be between 0 and 3.

x>-4 covers all the possible cases, and hence it must be true, whereas 0<x<3 only covers a few cases and can fail when x = -1, -2
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If |x - 2| < 5, which of the following must be true? 15 Jul 2026, 09:46
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I was confused a bit too. But look at the solution when you solve the actual equation that is |x-2| < 5. For this we get our solution as x lying between -3 and 7 non inclusive.
So, my answer rance is X E (-3,7)

Now we need to look at the options and figure out which of the options will always satisfy the solution that we got for X.
(A) x > 0 --> Not true as our x has negative values as well
(B) x > 8 --> Not true as our x is always less than 7
(C) x > -4 --> All values of x satisfy this condition. Every value in the range (-3,7) is greater than -4
(D) 0 < x < 3 --> This is a subset of the answer. We can have values of x which are greater than 3 and also values of x like -2,-1 which are smaller than 0.
DonZepp
I'm weirded out about the x > -4 answer. This answer states that x can be any value bigger than -3, so also e.g. x can be 10. But this doesn't suit the original constraint as in 10 > 7.

Please explain
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If |x - 2| < 5, which of the following must be true? 07 Aug 2026, 06:43
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I still believe that the right answer to this question just might be Option D.

This becomes a must be true question set which essentially means whatever option set that we do pick up, ideally all of the values should answer the question stem.
Option C satisfies every value above -3 and does not hold true for -3. But option D choices, all of them hold true and fall under must be tru.
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If |x - 2| < 5, which of the following must be true? 10 Aug 2026, 10:06
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Hi vrinda6,

I can see exactly where the logic flipped, and it's a really common one. You wrote that "whatever option we pick, all of its values should answer the question stem." That's the reverse of what a must be true question asks - and fixing that one direction settles the whole thing.

Which way the arrow points

The question isn't asking: do all the values in the option satisfy the inequality? It's asking: for every x that satisfies the inequality, is this statement always true?

So the master range is your solution set: -3 < x < 7 (as the earlier solutions established). The correct option must be a statement that holds for every single x in that range.

- C) x > -4: Take any x from -3 up to 7. Is it greater than -4? Always yes - the smallest values (like -2.9, -2, -1) are all still above -4. So C is true for the entire range. ✓
- D) 0 < x < 3: Now test the whole range against D. x = -1 is a valid solution to the inequality (|-1 - 2| = 3 < 5), but -1 is not between 0 and 3. So D fails for part of the range. ✗

That's the key: D's values do fit inside the range, but plenty of valid x values fall outside D. "All of D's values work" isn't what's being tested - "all valid x values satisfy the statement" is.

A quick parallel to lock the direction in

Suppose you're told x is an even number and asked what must be true:

- "x is an integer" - true for every even number. ✓ (this is the C-type answer)
- "x = 4" - sure, 4 is even, but not every even number is 4. ✗ (this is the D-type trap)

The right answer is the wider net that catches all cases - not the narrow one that only some cases fall into. Same reasoning makes C the answer here.

Answer: C

vrinda6
I still believe that the right answer to this question just might be Option D.

This becomes a must be true question set which essentially means whatever option set that we do pick up, ideally all of the values should answer the question stem.
Option C satisfies every value above -3 and does not hold true for -3. But option D choices, all of them hold true and fall under must be tru.
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