If a² + 7a < 0, then which one of the following could be the value of a?

Question: If a² + 7a < 0, then which one of the following could be the value of a?

Solution:
Given that, a² + 7a < 0
⇒ a(a + 7) < 0
For the product of two factors to be less than zero (negative), one factor must be positive and the other must be negative.

Case 1: a > 0 and (a + 7) < 0
⇒ a > 0 and a < -7 (Not possible)

Case 2: a < 0 and (a + 7) > 0
⇒ a < 0 and a > - 7
So, the range for a is: - 7 < a < 0.

Checking the options:
ক) - 3: -7 < -3 < 0 (True)
খ) 0: 0 is not less than 0 (False)
গ) 1: 1 is not less than 0 (False)
ঘ) 3: 3 is not less than 0 (False)

Therefore, the value of a could be - 3.