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Updated on: 30 Jun 2025, 23:47
Originally posted by MathRevolution on 25 Aug 2017, 01:17.
Last edited by Bunuel on 30 Jun 2025, 23:47, edited 1 time in total.
Last edited by Bunuel on 30 Jun 2025, 23:47, edited 1 time in total.
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C
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Difficulty:
55%
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Question Stats:
65% (02:08) correct
35%
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wrong
based on 1074
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Which of the following inequalities is equal to |x - 3|x|| < 8?
A. 0 < x < 4
B. 0 < x < 2
C. -2 < x < 4
D. -2 < x < 2
E. -2 < x < 0
A. 0 < x < 4
B. 0 < x < 2
C. -2 < x < 4
D. -2 < x < 2
E. -2 < x < 0
MathRevolution
Case 1: if \(x >0\) then \(|x| = x\), hence the equation can be written as
\(|x-3x|<8\), or \(|-2x|<8\) or \(2x<8\)
therefore \(x<4\)-----(1)
Case 2: if \(x<0\), then \(|x| = -x\), hence the equation can be written as
\(|x -3(-x)|<8\), or \(|x+3x|<8\), or \(|4x|<8\) or \(|x|<2\)
therefore \(-x<2\) or \(x>-2\)----(2)
Case 3: if \(x = 0\), then it will always satisfy the inequality
combining cases 1, 2 & 3 we get
\(-2<x<4\)
Option \(C\)
25 Aug 2017, 03:34
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MathRevolution
\(|x-3|x||<8 \iff -8 < x-3|x| < 8\)
Case 1: \(x \geq 0\)
We have \(-8 < x - 3x < 8 \implies -8 < -2x < 8 \implies 4 > x > -4\)
Thus \(0 \leq x < 4\)
Case 2: \(x < 0\)
We have \(-8 < x + 3x < 8 \implies -8 < 4x < 8 \implies -2 < x < 2\)
Thus \(-2 < x < 0\)
Combine both 2 cases, we have \(-2 < x < 4\). Answer C
