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What values of x will satisfy the inequality |x|-2/|x|+3≤0?

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What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   15 Nov 2019, 13:51
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What values of x will satisfy the inequality \(\frac{|x|-2}{|x|+3}≤0?\)
A) x∈ (-3,2)
B) x∈ (-∞, -3) ∪ (2, ∞)
C) x∈ (-3,3)
D) x∈ (-2,2)
E) x∈ (-∞, -3) ∪ (-2, ∞)
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D
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   15 Nov 2019, 20:32
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chetan2u wrote:
Asad wrote:
What values of x will satisfy the inequality \(\frac{|x|-2}{|x|+3}≤0?\)
A) x∈ (-3,2)
B) x∈ (-∞, -3) ∪ (2, ∞)
C) x∈ (-3,3)
D) x∈ (-2,2)
E) x∈ (-∞, -3) ∪ (-2, ∞)



\(\frac{|x|-2}{|x|+3}≤0\) will always have |x|+3>0, |x|-2≤0......|x|≤2.....
Thus x lies between -2 and 2.

D

Shouldn't this be [-2,2]; i.e. inclusive of -2 & 2?
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   18 May 2020, 21:27
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Here's how I solved it, please confirm if this method is correct.

\(\frac{|x|-2}{|x|+3}\) \(\leq{0}\).

Now, we know that the denominator will be positive no matter what. So, we can go ahead and multiply the whole inequality with |x|+3 to get |x|-2 \(\leq{0.\)

This implies that \(-2\leq{x\leq{2\), and hence the range [-2,2] is valid and the answer is (D).
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   15 Nov 2019, 20:26
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Asad wrote:
What values of x will satisfy the inequality \(\frac{|x|-2}{|x|+3}≤0?\)
A) x∈ (-3,2)
B) x∈ (-∞, -3) ∪ (2, ∞)
C) x∈ (-3,3)
D) x∈ (-2,2)
E) x∈ (-∞, -3) ∪ (-2, ∞)



\(\frac{|x|-2}{|x|+3}≤0\) will always have |x|+3>0, |x|-2≤0......|x|≤2.....
Thus x lies between -2 and 2.

D
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   22 Apr 2020, 04:49
LeoN88 wrote:
chetan2u wrote:
Asad wrote:
What values of x will satisfy the inequality \(\frac{|x|-2}{|x|+3}≤0?\)
A) x∈ (-3,2)
B) x∈ (-∞, -3) ∪ (2, ∞)
C) x∈ (-3,3)
D) x∈ (-2,2)
E) x∈ (-∞, -3) ∪ (-2, ∞)



\(\frac{|x|-2}{|x|+3}≤0\) will always have |x|+3>0, |x|-2≤0......|x|≤2.....
Thus x lies between -2 and 2.

D

Shouldn't this be [-2,2]; i.e. inclusive of -2 & 2?



Any thoughts on this VeritasKarishma / GMATNinja
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   23 Apr 2020, 01:14
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gaurav2m wrote:
LeoN88 wrote:
chetan2u wrote:
Asad wrote:
What values of x will satisfy the inequality \(\frac{|x|-2}{|x|+3}≤0?\)
A) x∈ (-3,2)
B) x∈ (-∞, -3) ∪ (2, ∞)
C) x∈ (-3,3)
D) x∈ (-2,2)
E) x∈ (-∞, -3) ∪ (-2, ∞)



\(\frac{|x|-2}{|x|+3}≤0\) will always have |x|+3>0, |x|-2≤0......|x|≤2.....
Thus x lies between -2 and 2.

D

Shouldn't this be [-2,2]; i.e. inclusive of -2 & 2?



Any thoughts on this VeritasKarishma / GMATNinja


Yes, it should be [-2,2]. None of the options satisfy.
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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   19 May 2020, 03:11
I feel there is a mistake here. That answer ought to be [-2 2]
Thank you.
Proof
Since |x|+3> 0 (a positive number), we can multiply both sides of the inequality by |x|+3 to get
|x|-2≤0
Implies
|x|≤2 implies -2≤x≤2
Hence [-2 2]

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Re: What values of x will satisfy the inequality |x|-2/|x|+3≤0? [#permalink] New post   04 Jun 2020, 23:38
The Ans is D.
Reason:
When we have such type of question where what we get as an answer is not present in the solution then we have to choose the option which is closest to the original solution.

Assuming value of x=3 and putting it in the equation the ans is wrong so B and E is out of scope.

So closest ans is option D.
Assuming value of x=-2.8 and putting it in the equation the ans is wrong so A and C is out of scope.
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Re: What values of x will satisfy the inequality |x|-2/|x|+30? [#permalink] New post   07 Dec 2023, 03:24
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Re: What values of x will satisfy the inequality |x|-2/|x|+30? [#permalink]
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