Question

If x and y are integers and – 5 ≤ x ≤ 6 and 4 ≤ y ≤ 9, then the minimum value of \(\frac{2x-y}{x} \) is____.

• A. -7
• B. -2
• C. 1
• D. \(\frac{19}{5}\)

Answer 1

The Correct Option is A

We need to find the minimum value of \(\frac{2x-y}{x}\)
The value of (2x – y) will be minimum when y is maximum. Also, we cannot assume ‘x’ to be negative because in that case the whole expression will become positive. ‘x’ cannot be 0.
So, we can see that the minimum value of \(\frac{2x-y}{x}\) will be at x = 1 and y = 9.
Required answer = \(\frac{2x-y}{x}=\frac{2-9}{1}=-7\)
So, the correct option is (A): -7