Solve the following inequalities (where [•] denotes greates…

Maths Fundamental of Mathematics Greatest Integer Function, Fractional Part & Signum Function Subjective Type

Published on: August 12, 2026

Solve the following inequalities (where [•] denotes greatest integer function and {•} represent fractional part function)

(i) [x + [x]] < 0 (ii) [2x 2 – x] < 1 (iii) {x} <

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The correct answer is:

CHECK THE SOLUTION.

(i) x ∈ (– ∞,0 ) (ii) x ∈

(iii) x ∈

Sol. (i) [x + [x]] < 0

⇒ [x] < 0 ⇒ x ∈ (– ∞,0 )

(ii) [2x 2 – x] < 1

⇒ 2x 2 – x – 1 < 0

⇒ x ∈ ( ,1)

(iii) x ∈

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