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If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the

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If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the  [#permalink]

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New post 07 Apr 2019, 21:20
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A
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E

Difficulty:

  5% (low)

Question Stats:

80% (01:20) correct 20% (01:51) wrong based on 89 sessions

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Concentration: Accounting, Finance
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Re: If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the  [#permalink]

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New post 07 Apr 2019, 22:38
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Bunuel wrote:
If \(|2x – 4|\) is equal to 2 and \((x – 3)^2\) is equal to 4, then what is the value of x?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5



Given,

\(|2x – 4|\) = 2

when 2x - 4 is positive,

2x - 4 = 2

x = 3.

when 2x - 4 is negative,

- 2x + 4 = 2

- 2x = -2

x = 1.

Again,

( x - 3)^2 = 4

| x - 3| = 2

when x - 3 is positive,

x - 3 = 2

x = 5.

when x - 3 is negative,

- x + 3 = 2

- x = -1

x = 1.

In both cases x = 1 .

Thus x = 1 is our answer.

A is the correct answer.
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Re: If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the  [#permalink]

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New post 07 Apr 2019, 23:23
Here (x-3)^2=4
Therefore x-3= 2 or X-3=-2
So X=5 or X=1

Now we have |2x-4|=2
Substitute both the X values above and check which gives us the answer
For X=5, we get |2x-4|=10-4=6 wrong
For X=1, we get |2-4|=2 correct
So answer is X=1

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Re: If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the  [#permalink]

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New post 08 Apr 2019, 01:04
Bunuel wrote:
If \(|2x – 4|\) is equal to 2 and \((x – 3)^2\) is equal to 4, then what is the value of x?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5


solve for \((x – 3)^2\) is equal to 4
(x-5)(x-1)
so\(|2x – 4|\) is equal to 2
IMO A
at x=1 we get
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Re: If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the   [#permalink] 08 Apr 2019, 01:04
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