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Solve for x: x7/x+12≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12)
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Updated on: 14 Oct 2019, 01:45
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61% (01:08) correct 39% (01:22) wrong based on 28 sessions
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Solve for x: \(\frac{x7}{x+12}\)≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12) ∪ [7, ∞) D) x∈ (∞, 7) ∪ (12, ∞) E) x∈ (12,7)
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Originally posted by Asad on 13 Oct 2019, 12:26.
Last edited by Asad on 14 Oct 2019, 01:45, edited 1 time in total.



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Re: Solve for x: x7/x+12≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12)
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13 Oct 2019, 14:56
Asad wrote: Solve for x: x7/x+12≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12) ∪ [7, ∞) D) x∈ (∞, 7) ∪ (12, ∞) E) x∈ (12,7) First, note that the 'set notation' used in the answers is very unGMATy. Limit answer choices to the standard <, >, = and so on. To the question: Under the assumption that what you intended to write was (x7)/(x+12) then it is sufficient for the numerator to equal or for both numerator and denominator to have equal signs. The first case gives x = 7 The second case gives x > 7 (both positive) or x < 12 (both negative). Putting them together gives answer choice (C)
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Re: Solve for x: x7/x+12≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12)
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15 Oct 2019, 02:26
This inequality can be turned into a quadratic inequality.
Before that, there's a tricky bit to these type of questions. The denominator.
\(\frac{x7}{x+12} ≥ 0\)
Test takers could potentially make mistakes because it is so easy to go wrong when you're in a rush. But this can be overcome with a little bit of observation.
The RHS is \(0\). So we ought to understand that the RHS should comply with this information. If the denominator of \(\frac{x7}{x+12}\) were to be zero, the LHS would be undefined. Thus, an important inference  \(x\)can never be equal to \(12\)
keeping this information in mind, one can proceed to simplify this expression.
multiply both sides of the inequality with \((x+12)^2\).
\(=> (x7)(x+12) ≥ 0\)
You'll arrive at the roots 7 and 12. Look at the inequality again and determine the sign. The ranges for x will be of the form \(x ≥ 7\) and \(x < 12\).
In terms of the format that the answer choices take
\(x ∈ (∞, 12)\) and \([7, ∞)\) Notice the circular bracket in\(x ∈ (∞, 12)\) indicating that x is not equal to 12.
The answer is C.




Re: Solve for x: x7/x+12≥0 A) x∈ [7, 12] B) x∈ [7, 11] C) x∈ (∞, 12)
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15 Oct 2019, 02:26






