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

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

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

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