Linear Inequations-4

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Solve the following equaitions: (i)1/(x - 2) < 0 (ii) (x + 1)/(x + 2) ≥ 1

Solution: (i) 1/(x – 2) < 0

=>x – 2 < 0 [since, a/b < 0 and a > 0 => b < 0]

=> x < 2

=> x ∈ (-∞, 2)

Hence, the solution set of the given inequation is (-∞, 2).

(ii) We have, (x + 1)/(x + 2) ≥ 1

=>(x + 1)/(x + 2) – 1 ≥ 0

=> (x + 1 – x – 2)/(x + 2) ≥ 0

=> -1/(x + 2) > 0

=> x + 2 < 0 [Since, a/b > 0 and a < 0 => b < 0]

=> x < -2

=> x ∈ (-∞, -2)

Hence, the solution set of the given inequation is (-∞, -2).

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