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Mathematics

Given, x + 2 ≤ x3+3\dfrac{x}{3} + 3 and x is a prime number. The solution set for x is :

  1. ∅

  2. {0}

  3. {1}

  4. {0, 1}

Linear Inequations

ICSE Sp 2025

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Answer

Solving the given equation :

⇒x+2≤x3+3⇒x−x3≤3−2⇒3x−x3≤1⇒2x3≤1⇒x≤32⇒x≤1.5\Rightarrow x + 2 \le \dfrac{x}{3} + 3 \\[1em] \Rightarrow x - \dfrac{x}{3} \le 3 - 2 \\[1em] \Rightarrow \dfrac{3x - x}{3} \le 1 \\[1em] \Rightarrow \dfrac{2x}{3} \le 1 \\[1em] \Rightarrow x \le \dfrac{3}{2} \\[1em] \Rightarrow x \le 1.5

Since, x is a prime number less than 1.5

Solution set is empty.

Hence, Option 1 is the correct option.

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