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x ≥ -1 and x ≥ x^5
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Updated on: 21 Jul 2019, 19:18
Updated on: 21 Jul 2019, 19:18
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Question Stats:
90% (01:59) correct
9% (01:39) wrong based on 22 sessions
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If \(x ≥ -1\) and \(x ≥ x^5\) which of the following must be the correct answer?
A. \(x > 1\)
B. \(0 < x < 1\)
C. \(0 ≥ x ≥ -1\)
D. \(x > 0\)
E. None of these.
A. \(x > 1\)
B. \(0 < x < 1\)
C. \(0 ≥ x ≥ -1\)
D. \(x > 0\)
E. None of these.
Show: :: OA
Actually I don't know the answer. 
In my opinion, it will be E. You are welcome to try. 
In my opinion, it will be E. You are welcome to try. 
Re: x ≥ -1 and x ≥ x^5
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Updated on: 22 Jul 2019, 11:04
Updated on: 22 Jul 2019, 11:04
2
I've placed spoiler tags in case you want to work out the answer with a little nudging rather than a lot.
It's always a good idea to start with the bottom and/or the top of a given range. What is the smallest possible legal value for x? Let's test that and see if we can knock out any answers.
A more comprehensive way to solve this problem would be to identify what specific values satisfy both inequalities.
-Jordan Wolbrum
It's always a good idea to start with the bottom and/or the top of a given range. What is the smallest possible legal value for x? Let's test that and see if we can knock out any answers.
Show: :: Testing our smallest legal value.
If x = -1, both the left and right inequality will hold, so -1 can be a viable option. That's enough to eliminate A, B, and D all by itself.
Show: :: Dealing with the remaining choices.
If we can find a case where x can be greater than 0, then we can also eliminate answer choice C. The simplest value to test is 1, and that will also work, so C cannot be correct. The answer is E.
A more comprehensive way to solve this problem would be to identify what specific values satisfy both inequalities.
Show: :: For which values does the right inequality hold?
The values of -1, 0, and 1 all work.
If x is less than -1, raising it to the fifth power will give us a smaller number. (Try -2.)
If x is between 0 and 1, raising it to the fifth power will give us a smaller number. (Try -\(\frac{1}{2}\).)
Combined with the left inequality, our legal values for x are now -1 and \(1 ≥ x ≥ -0\).
If x is less than -1, raising it to the fifth power will give us a smaller number. (Try -2.)
If x is between 0 and 1, raising it to the fifth power will give us a smaller number. (Try -\(\frac{1}{2}\).)
Combined with the left inequality, our legal values for x are now -1 and \(1 ≥ x ≥ -0\).
-Jordan Wolbrum
Re: x ≥ -1 and x ≥ x^5
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22 Jul 2019, 02:14
22 Jul 2019, 02:14
1
Expert Reply
Hi,
your explanation is quite good. However, I do not understand the meaning of usage of the spoiler tag and not a straight explanation.
regards
your explanation is quite good. However, I do not understand the meaning of usage of the spoiler tag and not a straight explanation.
regards
