Question

If -1 ≤ a ≤ 2 and 1 ≤ b ≤ 3, then least possible value of (2a – 3b) is:

Answer 1

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Answer 2

The least possible value of (2a – 3b) is -11.

Given:

-1 ≤ a ≤ 2 and 1 ≤ b ≤ 3.

To Find:

The least possible value of (2a - 3b).

Solution:

We are given that -1 ≤ a ≤ 2 and 1 ≤ b ≤ 3.

We need to find the least possible value of (2a - 3b).

Now, (2a – 3b) = 2a + (-3b)

For (2a – 3b) = 2a + (-3b) to be minimum, the entire value must be negative.

Hence both the terms, (2a) and (-3b) must be negative.

For (2a) to be negative, 'a' must be negative. The least possible value of a such that (2a) is negative is a = -1.

For (-3b) to be negative, 'b' must be positive. The maximum value of 'b' for (-3b) to be the least is b = 3.

Hence, the least possible value of (2a – 3b) = (2x-1) + (3x-3) = -11.

∴ The least possible value of (2a – 3b) is -11.

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