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

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Bunuel
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If x ≠ 2.5 and 2x = |15 - 4x|, then x = [#permalink] New post   22 Oct 2018, 01:26
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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
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E
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BrentGMATPrepNow
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x = [#permalink] New post   05 Aug 2020, 10:10
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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


There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Given: |15 - 4x| = 2x
So, EITHER 15 - 4x = 2x OR 15 - 4x = -2x
Let's test each case.

Take: 15 - 4x = 2x
Add 4x to both sides: 15 = 6x
Solve: x = 15/6 = 5/2 = 2.5
Since we're told x ≠ 2.5, we can stop pursuing this case

Take: 15 - 4x = -2x
Add 4x to both sides: 15 = 2x
Solve: x = 15/2 = 7.5
NOTE: Since we've already seen that x = 2.5 is NOT a solution, we can be certain (without testing) that the correct answer must be x = 7.5

Answer: E

Cheers,
Brent
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x = [#permalink] New post   22 Oct 2018, 01:34
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] New post   22 Oct 2018, 04:57
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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] New post   23 Oct 2018, 07:20
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x = [#permalink] New post   23 Oct 2018, 19:26
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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] New post   07 May 2020, 11:20
If x ≠ 2.5 and 2x = |15 - 4x|, then x =?
Case 1: let,(15 - 4x) ≥ 0 [ |15 - 4x| = (15 - 4x) ] [ x ≤ 3.75 ]
so,2x = 15 - 4x
or,6x = 15
or,x = 2.5 ( given, x ≠ 2.5)

Case 2: (15 - 4x) <0 [ |15 - 4x| = -(15-4x ) ] [ x > 3.75]
2x = -(15 - 4x)
or,2x = -15 + 4x
or,-2x = -15
or,x = 7.5 ( satisfies our range )

correct answer E
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Re: If x ≠ 2.5 and 2x = |15 - 4x|, then x = [#permalink]
07 May 2020, 11:20
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