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Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al

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Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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New post 19 Mar 2019, 00:24
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:40) correct 27% (01:37) wrong based on 26 sessions

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Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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New post 19 Mar 2019, 00:47

Solution


Given:
    • The expression 8xy - 12y + 2x - 3 = 0 is true for all values of y

To find:
    • The value(s) of x

Approach and Working:
We can simplify the given expression in the following manner:
    • 8xy - 12y + 2x - 3 = 0
    Or, 4y (2x – 3) + 1 (2x – 3) = 0
    Or, (2x – 3) (4y + 1) = 0

As it is true for all values of y, we can say 2x – 3 = 0, which implies x = 3/2

Hence, the correct answer is option D.

Answer: D

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Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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New post 19 Mar 2019, 19:19
The easiest way I found was:

Given that "true for all values of y" take y as 1.

\(8x(1) - 12(1) + 2x - 3 = 0\)

\(10x - 15 = 0\)

Test the values...

\(10*\frac{3}{2} - 15 = 0\) ... Only option

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Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al  [#permalink]

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New post 19 Mar 2019, 20:23
Bunuel wrote:
Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for all values of y.

(A) 2/3
(B) 3/2 or -1/4
(C) -2/3 or -1/4
(D) 3/2
(E) -3/2 or -1/4


For 8xy - 12y + 2x - 3 = 0 to be true for all value of y, the constant term should be 0 and the y terms should be 0 too.
2x - 3 = 0
which gives x = 3/2
The y terms y(8x - 12) will be 0 too when x = 3/2.

Answer (D)
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Re: Find the value(s) of x such that 8xy - 12y + 2x - 3 = 0 is true for al   [#permalink] 19 Mar 2019, 20:23
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