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10 Apr 2026, 13:19
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Difficulty:
65%
(hard)
Question Stats:
59% (01:56) correct
41%
(01:41)
wrong
based on 145
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The number of integral solutions of the inequality |x-5|+|x-1|<2 is
A) 4
B) 0
C) 1
D) 2
E)3
A) 4
B) 0
C) 1
D) 2
E)3
11 Apr 2026, 11:45
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I would guess 0. Not sure of this answer because the questions asks for the "integral" solutions and I am not familiar with the word, Chatgpt says it's correct.
|x−5| + |x−1| < 2 is the distances from x to 5 and 1 on the number line.
The minimum possible value of occurs when x lies between 1 and 5 : |x−5|+|x−1|= (5−x)+(x−1)=4
So the smallest value the expression can take is 4. Otherwise, the sum becomes larger.
Since the inequality should be inferior to 2, and the minimum is already 4, there are no values of x that satisfy it.
|x−5| + |x−1| < 2 is the distances from x to 5 and 1 on the number line.
The minimum possible value of occurs when x lies between 1 and 5 : |x−5|+|x−1|= (5−x)+(x−1)=4
So the smallest value the expression can take is 4. Otherwise, the sum becomes larger.
Since the inequality should be inferior to 2, and the minimum is already 4, there are no values of x that satisfy it.
15 Apr 2026, 20:32
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Approached this question by plugging in different values for x ex.. 0,-1, 1, 5,6,7,-5.. in all scenarios, equation is not possible..
So answer is no solution B
So answer is no solution B
