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Re: If |p−6|+p=6, which of the following must be true? [#permalink]

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30 Jun 2013, 18:08

1

This post received KUDOS

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

There are two ways to solve, one of which is to just pick numbers.

The other way: |p-6|+p=6 |p-6| = 6-p |p-6| = -(p-6) |x| = -x (i.e. the value inside the absolute value bars is negative) So, (p-6) is negative when p≤6

Re: If |p−6|+p=6, which of the following must be true? [#permalink]

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01 Jul 2013, 14:39

without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6? the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6? the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

thanks!

Because when \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\).

We have \(|p-6|=-(p-6)\), thus \(p-6\leq{0}\) --> \(p\leq{6}\).
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Re: If |p−6|+p=6, which of the following must be true? [#permalink]

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09 Aug 2014, 13:26

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