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07 Nov 2022, 07:51
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Traj201090
If x = 0, then we get:
- 0 = -|0|
0 = 0.
If x = -5, then we get:
- -5 = -|-5|
-5 = -5.
15 Aug 2023, 21:43
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Bunuel
Hi Bunuel, this is semi-related to the question, but is lx-2l always going to equal l2-xl? If so, how do I make sense of it? It seems to be true when I plug in numbers. Is this a known property for all real numbers such that l2-xl = l-(x-2)l and since l-(x-2)l=lx-2l, l2-xl=lx-2l would this work?
This is in relation to this problem I saw online:
What is the value of |x−2|?
(1) |x−4|=2
(2) |2−x|=4
Answer was B (2) is sufficient.
16 Aug 2023, 00:40
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sctutor
Indeed, the property |a - b| = |b - a| holds true for all a and b. Think of |a - b| as the distance between a and b on the number line. Similarly, |b - a| represents the distance between b and a on the same line. Naturally, these two distances are identical.
Back to your problem:
What is the value of |x − 2|?
(1) |x − 4| = 2
Here, x could be 6 or 2. If x = 6, |x − 2| = 4. However, if x = 2, |x − 2| = 0. Two different answers. Not sufficient.
(2) |2 − x| = 4
Since |2 − x| = |x − 2| for all x, then the above statement directly gives the value of |x − 2|. Sufficient.
Alternatively, |2 − x| = 4 implies x could be -2 or 6. Both yield the same value of 4 for |x − 2|. Sufficient.
Answer: B.
Hope it helps.
