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If |p 6| + p = 6, which of the following must be true? 16 Jun 2015, 07:44
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Bunuel
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Hi Bunuel,

if we substitute p=0 then the answer must be 6. There can be no other answer right?

Not sure I understand what you mean...

p = 0, as well as any other value of p less than or equal 6 satisfies |p − 6| + p = 6.
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thanks Bunuel..i have got it now... i wasn't seeing it the right way!!
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If |p 6| + p = 6, which of the following must be true? 16 Jun 2015, 08:58
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arshu27
Hi Bunuel,

if we substitute p=0 then the answer must be 6. There can be no other answer right?
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You are wrong here Ashu,

There can be infinite many answers for this equation and the answer will fall in the range 0<p<6

I hope it answers your query!
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If |p 6| + p = 6, which of the following must be true? 16 Sep 2017, 16:28
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It's simple property of Absolute Value: if \(|x| = y\), then \(y>= 0\);

Here the given equation can be rearranged as, \(|p-6| = 6-p\)
which implies, \(6-p >=0\)
or \(p<=6\). Hence E.

I hope this clarifies some doubts.
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If |p 6| + p = 6, which of the following must be true? 26 Apr 2022, 10:23
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|a-b| = |b-a| = the DISTANCE between b and a
b-a = the DIFFERENCE between b and a
Rule:
The distance between two values will be equal to the difference between the two values as long as the difference is NONNEGATIVE.

bagdbmba
If |p−6|+p=6, which of the following must be true?

A. p=0
B. p=-6
C. p=6
D. p>-6
E. p<=6
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|p−6|+p=6
|6-p| = 6-p
In words:
The distance between 6 and p is equal to the difference between 6 and p.
Since distance = difference as long as the difference is nonnegative, we get:
6-p ≥ 0
6 ≥ p

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If |p 6| + p = 6, which of the following must be true? 31 Aug 2023, 04:19
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bagdbmba
Bunuel
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Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?

When \(p\leq{6}\), then \(|p-6|=-(p-6)=6-p\).
When \(p\geq{6}\), then \(|p-6|=p-6\).

So, only 6 satisfies both |p−6|= (p-6) and |p−6|=-(p-6)

Then why the answer is not ONLY 6 for the above qs?
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Because 6 is a solution definitely, but that is not the only solution, any value less than or equal to 6 is possible for this question. You have to address all solution particularly when all solutions is given in the question.

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If |p 6| + p = 6, which of the following must be true? 29 Sep 2025, 18:30
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