Absolute is easy, right?

Algebra Level 1

How many integers x x satisfy the inequality ∣ 5 8 − x ∣ < − 1 \large \left | \frac{5}{8-x} \right | < -1


The answer is 0.

Irvan Ary Maulana Nugroho by Irvan Ary Maulana Nugroho , 20

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1 solution

Michael Fuller
Mar 8, 2016

The LHS is an absolute value, so ∣ 5 8 − x ∣ ≥ 0 \large \left | \frac{5}{8-x} \right | \ge 0 . This contradicts ∣ 5 8 − x ∣ < − 1 \large \left | \frac{5}{8-x} \right | < -1 , so there are no values of x x at all that satisfy the equation.

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