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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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Math Expert
Joined: 02 Sep 2009
Posts: 58396
If |2x – 4| is equal to 2 and (x – 3)2 is equal to 4, then what is the  [#permalink]

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07 Apr 2019, 21:20
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5% (low)

Question Stats:

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

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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

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Joined: 31 Oct 2013
Posts: 1467
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
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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07 Apr 2019, 22:38
1
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.

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Joined: 04 Aug 2016
Posts: 8
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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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

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Concentration: Sustainability, Marketing
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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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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
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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