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09 Sep 2024, 12:44
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Difficulty:
15%
(low)
Question Stats:
84% (01:08) correct
15% (00:48) wrong based on 13 sessions
History
Date
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How many integers are in the solution set of the inequality \(x^2 - 10 < 0\)?
A. Two
B. Five
C. Six
D. Seven
E. Ten
A. Two
B. Five
C. Six
D. Seven
E. Ten
26 Oct 2024, 10:23
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OE
The inequality x2 - 10 < 0 is equivalent to x2 < 10. By inspection, the positive integers that satisfy this inequality are 1, 2, and 3. Note that 0 and the negative integers -1, -2, and -3 also satisfy the inequality, and there are no other integer solutions. So there are seven integers in the solution set: -3, -2, -1, 0, 1, 2, and 3. Thus the correct answer is Choice D.
The inequality x2 - 10 < 0 is equivalent to x2 < 10. By inspection, the positive integers that satisfy this inequality are 1, 2, and 3. Note that 0 and the negative integers -1, -2, and -3 also satisfy the inequality, and there are no other integer solutions. So there are seven integers in the solution set: -3, -2, -1, 0, 1, 2, and 3. Thus the correct answer is Choice D.
03 Jul 2025, 19:58
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\(x^2 – 10 < 0\)
=> \(x^2 < 10\)
Taking square root on both the sides we get
|x| < \(\sqrt{10}\) [ watch this video to MASTER Absolute Values ]
=> |x| < 3.2 (approximately)
=> -3.2 < x < 3.2
Given that x is integer
=> Possible values of x are -3, -2, ..., 2, 3
=> 3 - (-3) + 1 = 6 + 1 = 7 values
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Inequalities
=> \(x^2 < 10\)
Taking square root on both the sides we get
|x| < \(\sqrt{10}\) [ watch this video to MASTER Absolute Values ]
=> |x| < 3.2 (approximately)
=> -3.2 < x < 3.2
Given that x is integer
=> Possible values of x are -3, -2, ..., 2, 3
=> 3 - (-3) + 1 = 6 + 1 = 7 values
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Inequalities
