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04 May 2021, 08:15
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A
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Difficulty:
25%
(medium)
Question Stats:
75% (01:35) correct
25%
(01:48)
wrong
based on 512
sessions
History
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How many integer solutions are there to the inequality \(|x+8|<x\)?
A. 0
B. 2
C. 3
D. 8
E. 16
A. 0
B. 2
C. 3
D. 8
E. 16
25 Sep 2024, 06:18
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PrinceDAYAL
How many integer solutions are there to the inequality \(|x+8|<x\)?
A. 0
B. 2
C. 3
D. 8
E. 16
x cannot be negative because a negative number, x, cannot be greater than the non-negative value of |x + 8|.
x cannot be 0, because |0 + 8| = 8, and 8 is not less than 0.
For positive x, since x + 8 > 0, we'd have |x + 8| = x + 8. Thus, when x is positive, the inequality becomes x + 8 < x, which simplifies to 8 < 0, which is not correct. Therefore, for positive x, the inequality also does not have a solution.
Answer: A.
General Discussion
04 May 2021, 08:26
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Bunuel
\(|x+8|<x\)
-x < x + 8 < x
-x - 8 < x < x - 8
-8 < x < -8
IMO, A = 0
