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28 Mar 2019, 01:42
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:55) correct
20%
(02:10)
wrong
based on 599
sessions
History
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Not Attempted Yet
Which of the following is the solution set for the inequality \(0<|x|-2x<3\)?
A. \(-1<x<0\)
B. \(0<x<1\)
C. \(1<x<2\)
D. \(2<x<3\)
E. \(3<x<4\)
A. \(-1<x<0\)
B. \(0<x<1\)
C. \(1<x<2\)
D. \(2<x<3\)
E. \(3<x<4\)
31 Mar 2019, 14:39
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\(0 < |x| -2x < 3\)
Case A: \(x ≥ 0\)
\(0 < -x < 3\)
\(-3 < x< 0\)
There are no solutions here since \(x ≥ 0\).
Case B: \(x < 0\)
\(0 < -3x < 3\)
\(0 < -x < 1\)
\(-1 < x < 0\)
That's what we were looking for. Hence, \(A\).
Case A: \(x ≥ 0\)
\(0 < -x < 3\)
\(-3 < x< 0\)
There are no solutions here since \(x ≥ 0\).
Case B: \(x < 0\)
\(0 < -3x < 3\)
\(0 < -x < 1\)
\(-1 < x < 0\)
That's what we were looking for. Hence, \(A\).
General Discussion
28 Mar 2019, 04:08
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MathRevolution
We can PLUG IN THE ANSWERS, which represent the range of x.
A: -1 < x < 0
Plugging x=-0.5 into the given inequality, we get:
0 < |-0.5| - 2(-0.5) < 3
0 < 0.5 + 1 < 3
0 < 1.5 > 3
Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its range.
Eliminate B, C, D and E.
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