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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

|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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bagdbmba
Bunuel
debayan222
Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?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?

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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