Question 10

The number of integral solutions of the inequation $$\left|\frac{2}{x-13}\right| > \frac{8}{9}$$ is

Solution

The inequality rearranges to $$|x-13| < \frac{9}{4} = 2.25$$ with $$x \neq 13$$. The integers satisfying $$10.75 < x < 15.25$$, excluding $$13$$ [as at $$x=13$$ the denominator of original inequation is undefined], are $$11, 12, 14, 15$$, giving $$4$$ integral solutions.

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