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