Question 5
Find the number of integer solutions to $$\left| |x| - 2020 \right| < 5$$.
Correct Answer: 18
Solution
The inequality means $$-5 < |x| - 2020 < 5$$, so $$2015 < |x| < 2025$$. The integer values of $$|x|$$ are $$2016, 2017, \ldots, 2024$$, which is 9 values. Each gives two integers $$x$$ of opposite signs, so there are $$9 \times 2 = 18$$ solutions.
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