Q21

Q21 - Find the number of integer solutions to ||x| - 2000| < 5.
Answer: 18

Solution:
|y| < 5 => -5 < y < 5
-5 < y => |x| - 2000 > -5 => |x| > 1995 => x < -1995 U x > 1995_____[1]
y < 5 => |x| - 2000 < 5 => |x| < 2005 => -2005 < x < 2005________[2]

We need to find intersection of [1] and [2].
LHS => -2005 < x< -1995 => x has 9 values in this region.
RHS => 1995 < x < 2005 => x has 9 values in this region.
Answer: 9 + 9 = 18.

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