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If x ≠ 2.5 and 2x = |15 - 4x|, then x =

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Math Expert
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Joined: 02 Sep 2009
Posts: 53065
If x ≠ 2.5 and 2x = |15 - 4x|, then x =  [#permalink]

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New post 22 Oct 2018, 00:26
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

99% (01:00) correct 1% (02:12) wrong based on 84 sessions

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Director
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =  [#permalink]

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New post 22 Oct 2018, 00:34
Bunuel wrote:
If x ≠ 2.5 and 2x = |15 - 4x|, then x =

A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5


Given, |15 - 4x|= 2x
Or, -(15-4x)=2x; ( |15-4x|=-(15-4x) when (15-4x)<0 or, 15<4x or,x>3.75 )
Or, 4x-15=2x
Or, 2x=15
Or, x=7.5

Ans. (E)
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =  [#permalink]

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New post 22 Oct 2018, 03:57
2x= |15-4x| means 2x= 15-4x; 2x+6x= 15; 8x= 15; x= \(\frac{15}{6}\)= 2.5 (Not Possible given)

OR

2x= |15-4x| means 2x= -(15-4x); 2x= -15+4x; 2x= 15; x= \(\frac{15}{7}\)= 7.5

Answer: E
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =  [#permalink]

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New post 23 Oct 2018, 06:20
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =  [#permalink]

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New post 23 Oct 2018, 18:26
Bunuel wrote:
If x ≠ 2.5 and 2x = |15 - 4x|, then x =

A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5


With an absolute value equation, we must consider two cases:

Case 1: Solve for x when 15 - 4x is positive :

2x = 15 - 4x

6x - 15

x = 2.5 (but we are given that x ≠ 2.5)

Case 2: Solve for x when 15 - 4x is negative:

2x = -(15 - 4x)

2x = -15 + 4x

-2x = -15

x = 7.5

Answer: E
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x =   [#permalink] 23 Oct 2018, 18:26
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If x ≠ 2.5 and 2x = |15 - 4x|, then x =

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