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24 Sep 2018, 00:50
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (01:43) correct
36%
(01:32)
wrong
based on 1300
sessions
History
Date
Time
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Not Attempted Yet
\(\frac{4}{x}<-\frac{1}{3}\), what is the range of x?
A. \(-12<x\)
B. \(12>x>0\)
C. \(x>0\)
D. \(-12<x<0\)
E. \(x<0\)
A. \(-12<x\)
B. \(12>x>0\)
C. \(x>0\)
D. \(-12<x<0\)
E. \(x<0\)
T1101
\(\frac{4}{x}<-\frac{1}{3}\), what is the range of x?
A. \(-12<x\)
B. \(12>x>0\)
C. \(x>0\)
D. \(-12<x<0\)
E. \(x<0\)
A. \(-12<x\)
B. \(12>x>0\)
C. \(x>0\)
D. \(-12<x<0\)
E. \(x<0\)
Method 1:
\(\frac{4}{x}<-\frac{1}{3}\)
\(\frac{4}{x} + \frac{1}{3} < 0\)
\(\frac{x + 12}{3x} < 0\)
-12 < x < 0
Answer (D)
Method 2:
\(\frac{4}{x}<-\frac{1}{3}\)
x can be positive, or negative so we need to take two cases:
Case 1: If x > 0, multiply both sides by 3x without flipping the inequality sign
\(12 < -x\)
Multiply both sides by -1 (this will flip the inequality sign)
\(x < -12\)
But x was assumed to be non negative here so we have no solution in this range.
Case 2: If x < 0, multiply both sides by 3x by flipping the inequality sign.
\(12 > -x\)
Multiply both sides by -1 (this will flip the inequality sign)
\(x > -12\)
So here, -12 < x < 0
Answer (D)
09 Oct 2018, 22:52
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From the question stem we can conclude that x<0.
If we move x to the other side of the inequality, it changes sign (as we multiply with a negative):
4>\(-(\frac{1}{3})x\)
From here we can conclude that the maximum value x can be is -12, in order to make the inequality true.
Hence -12<x<0.
If we move x to the other side of the inequality, it changes sign (as we multiply with a negative):
4>\(-(\frac{1}{3})x\)
From here we can conclude that the maximum value x can be is -12, in order to make the inequality true.
Hence -12<x<0.
-12 < x < 0
