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Question: Number of integral values of x satisfying the in equation \(\frac{x}{x + 2}\)£\(\frac{1}{|x|}\) is...

Number of integral values of x satisfying the in equation

xx+2\frac{x}{x + 2}£1∣x∣\frac{1}{|x|} is

A

2

B

8

C

4

D

3

Answer

4

Explanation

Solution

x∣x∣x+2\frac{x|x|}{x + 2} £ 1

x∣x∣−x−2x+2\frac{x|x| - x - 2}{x + 2} £ 0

Case I xÎ [0, ¥) x2−x−2x+2\frac{x^{2} - x - 2}{x + 2} £ 0

̃ (x−2)(x+1)x+2\frac{(x - 2)(x + 1)}{x + 2} £ 0

̃ x £ 2

̃ integral values 0, 1, 2

Case II x Î (–¥, 0) −x2−x−2x+2\frac{- x^{2} - x - 2}{x + 2} £ 0

̃ x > – 2

̃ x = – 1

So 4 integral values