Question

$|x - 1| \div x + 2 < 1$
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Answer 1

Answer:

| x - 1 | / (x + 2) < 1

» According to the given condition,

(x + 2) ≠ 0

» x ≠ - 2

If (x + 2) is negative,

» (x + 2) < 0

» x < - 2

Therefore, multiply both sides by (x + 2)

» | x - 1 | > x + 2

» Since, x + 2 is negative

» |x - 1| ≥ 0

» x - 1 ≥ 0 or x - 1 ≤ 0

» x ≥ 1 or x ≤ 1

Hence, x = (-∞, ∞)

If (x + 2) is positive.

» | x - 1 | < x + 2, also ≠ 0

» | x - 1 | < 0

It's not possible.

Therefore, x = R - {-2} is the solution.