Question

Given, `x + 2 ≤ x/3 + 3` and x is a prime number. The solution set for x is ______.

Options

• ∅

• {0}

• {1}

• {0, 1}

Answer 1

Given, `x + 2 ≤ x/3 + 3` and x is a prime number. The solution set for x is ∅.

Explanation:

`x + 2 ≤ x/3 + 3`

⇒ `x - x/3 ≤ 3 - 2`

⇒ `(3x - x)/3 ≤ 1`

⇒ `(2x)/3 ≤ 1`

⇒ `x ≤ 3/2`

⇒ x ≤ 1.5

Since, x is a prime number less than 1.5.

Solution set is empty.