Solve for x, the inequalities Exercises. |x-2|-1 |x-2|-2 0 - Vidyadip

Question

Solve for x, the inequalities Exercises.
$\frac{|\text{x}-2|-1}{|\text{x}-2|-2}\leq0$

✓

Answer

Given that $\frac{|\text{x}-2|-1}{|\text{x}-2|-2}\leq0$
Put $|\text{x}-2|=\text{y}$
⇒ y - 1 > 0, y - 2 < 0
⇒ y > 1, y < 2
⇒ 1 < |x - 2|, |x - 2| < 2
⇒ x - 2 < -1 or x - 2 > 1 and - 2 < x -2 < 2
⇒ x < 1 or x > 3 and 0 < x < 4
Hence, the required solution is (0, 1) (3, 4).

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