Question

Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` is ______.

Options

• 6

• 7

• 8

• Infinite

Answer 1

Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` is 7.

Explanation:

`(3/4)^(6x + 10 - x^2) < (3/4)^3`

⇒ 6x + 10 – x² > 3

⇒ x² – 6x – 7 < 0

⇒ (x + 1)(x – 7) < 0

⇒ x ∈ (–1, 7)

⇒ Number of integral values of x = 7