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# If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x =

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Math Expert
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If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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20 Oct 2017, 00:13
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Difficulty:

15% (low)

Question Stats:

93% (00:54) correct 7% (01:41) wrong based on 68 sessions

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If $$(6 + \frac{2}{x})(x - 4) = 0$$, and x does not equal 4, then x =

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3
[Reveal] Spoiler: OA

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If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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20 Oct 2017, 01:03
Bunuel wrote:
If $$(6 + \frac{2}{x})(x - 4) = 0$$, and x does not equal 4, then x =

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

$$(6 + \frac{2}{x})(x - 4) = 0$$

$$6x - \frac{8}{x} - 24 + 2 = 0$$

$$6x - \frac{8}{x} - 22 = 0$$

$$6x^2 - 22x - 8 = 0$$

$$6x^2 - 24x + 2x - 8 = 0$$ => $$6x(x - 4) + 2(x - 4) = 0$$ => $$(6x+2)(x-4) = 0 => x=4$$ or $$-\frac{1}{3}$$

Since x cannot be 4, the other value of x = $$-\frac{1}{3}$$(Option C)
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Senior Manager
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Re: If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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20 Oct 2017, 04:37
(6+$$\frac{2}{x}$$)(x-4)=0
$$\frac{(6x+2)}{x}$$ * (x-4)=0
(6x+2) * (x-4)=0 ---Cross multiplying by x
Therefore, x = $$\frac{-2}{6}$$ = $$\frac{-1}{3}$$ or 4
Since x is not equal to 4, x = $$\frac{-1}{3}$$
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If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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20 Oct 2017, 07:37
Bunuel wrote:
If $$(6 + \frac{2}{x})(x - 4) = 0$$, and x does not equal 4, then x =

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

You do not have to do much math here. Set the first term equal to 0 and you have your answer.

By the zero product rule, if
a * b = 0, then a = 0, or b = 0, or both = 0

x does not equal 4. Hence
(x - 4) cannot = 0. Therefore:

The first term, $$(6 + \frac{2}{x})$$ must equal 0.

(Plain English: you cannot have a product of 0 unless one or both of the factors is 0.)

$$(6 + \frac{2}{x}) = 0$$

$$6 = - \frac{2}{x}$$

$$6x = - 2$$

$$x = -\frac{2}{6} = -\frac{1}{3}$$

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Intern
Joined: 30 May 2017
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Re: If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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20 Oct 2017, 09:34
If x cannot be 4, (6+2/x) must be equal 0 to multiply (x-4) and obtain zero.

6+ 2/x = 0
2/x = -6
x = - 1 / 3

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Re: If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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24 Oct 2017, 06:16
Bunuel wrote:
If $$(6 + \frac{2}{x})(x - 4) = 0$$, and x does not equal 4, then x =

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

Since x ≠ 4, we see that x - 4 can’t be 0, and therefore, in order for the product to equal 0, 6 + 2/x must equal 0:

6 + 2/x = 0

2/x = -6

2 = -6x

-1/3 = x

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Re: If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x = [#permalink]

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27 Oct 2017, 09:13
I got C, but I was an idiot of massive proportions and totally missed the shortcut. The hint is that (x-4) will not give you zero. Hence, you only need to solve for (6+[2][/x])=0.

I am guessing this cost me about 50 seconds and unneeded stress.
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I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

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Re: If (6 + 2/x)(x - 4) = 0, and x does not equal 4, then x =   [#permalink] 27 Oct 2017, 09:13
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