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# If |x − 2| = p, where x < 2, then x − p =

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Manager
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Joined: 02 Nov 2018
Posts: 118
If |x − 2| = p, where x < 2, then x − p =  [#permalink]

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14 Mar 2019, 22:14
00:00

Difficulty:

65% (hard)

Question Stats:

43% (01:34) correct 57% (01:30) wrong based on 23 sessions

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If |x − 2| = p, where x < 2, then x − p =

(A) −2

(B) 2

(C) 2 − 2p

(D) 2p − 2

(E) |2p − 2|

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Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 118
Re: If |x − 2| = p, where x < 2, then x − p =  [#permalink]

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14 Mar 2019, 22:15
Since x < 2, it follows that |x − 2| = 2 − x.
If 2 − x = p, then
x = 2 − p.
Thus x − p = 2 − 2p.
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Manager
Joined: 12 Sep 2017
Posts: 183
Re: If |x − 2| = p, where x < 2, then x − p =  [#permalink]

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15 Mar 2019, 18:32
TyrionLannister wrote:
Since x < 2, it follows that |x − 2| = 2 − x.
If 2 − x = p, then
x = 2 − p.
Thus x − p = 2 − 2p.

TyrionLannister

Hello!

Could you be so kind and clarify why is it 2 - 2p? Based in your answer it can also be 2.

|x − 2| = 2 − x.

Case 1: x = p + 2
Case 2: x = 2 - p

x - p

Case 1: p + 2 - p = 2
Case 2: 2 - p - p = 2 - 2p

Kind regards!
Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 118
If |x − 2| = p, where x < 2, then x − p =  [#permalink]

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15 Mar 2019, 22:17
1
hi jfranciscocuencag

as you see,
we find x = 2 − p.
now subtract p from both side , then we find
x − p = 2 − 2p{ subtract p from both side}
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If |x − 2| = p, where x < 2, then x − p =   [#permalink] 15 Mar 2019, 22:17
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