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14 Mar 2012, 12:42
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D
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Difficulty:
75%
(hard)
Question Stats:
41% (01:40) correct
59%
(01:52)
wrong
based on 554
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What is the solution set for the inequality -2|3-2x| < 14?
A. -11/2 < x < 17/2
B. -5 < x < 2
C. -2 < x < 5
D. All values of x satisfy the inequality
E. No values of x satisfy the inequality
A. -11/2 < x < 17/2
B. -5 < x < 2
C. -2 < x < 5
D. All values of x satisfy the inequality
E. No values of x satisfy the inequality
14 Mar 2012, 13:03
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What is the solution set for the inequality \(-2|3-2x| < 14?\)
A. -11/2 < x < 17/2
B. -5 < x < 2
C. -2 < x < 5
D. All values of x satisfy the inequality
E. No values of x satisfy the inequality
\(-2*|3-2x|=negative*nonnegative=nonpositive\), which is ALWAYS less than positive number 14. So, this inequality holds true for any \(x\).
Answer: D.
A. -11/2 < x < 17/2
B. -5 < x < 2
C. -2 < x < 5
D. All values of x satisfy the inequality
E. No values of x satisfy the inequality
\(-2*|3-2x|=negative*nonnegative=nonpositive\), which is ALWAYS less than positive number 14. So, this inequality holds true for any \(x\).
Answer: D.
16 Mar 2012, 04:27
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shankar245
If you do it properly you'll get the same answer. But you don't need that.
Consider this: \(-2*|3-2x|<14\) --> reduce by negative -2 and flip the sign: \(|3-2x|>-7\) --> LHS is an absolute value, which is always nonnegative, so \(|3-2x|\) will always be more than negative -7, so it'll be more for all values of \(x\).
Hope it's clear.
