What is the solution to the inequality √(2x) < 1 + x ?
A) ∀x ≥ 0
B) ℝ
C) ∅
D) ∀x > 0
E) ∀x ≠ 0
IMAT 2025 · Question 48
Q48 - Algebraic inequalities
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The correct answer is A) ∀x ≥ 0.
The square root only exists for x ≥ 0. In that range both sides are positive, so you can square:
2x < 1 + 2x + x² → 0 < 1 + x²
That's always true. So the inequality holds for every x ≥ 0, and x = 0 works too (0 < 1), which rules out D.
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