If - 3 ≤ x ≤ 5 and - 5 ≤ y ≤ 3, what is the smallest value of (2x - y)?

Solution:

To find the smallest value of the expression 2x - y, we need to analyze the possible values for x and y within their respective ranges.

Given:

- 3 ≤ x ≤ 5

- 5 ≤ y ≤ 3

We want to minimize the expression:

2x - y

Step 1: Determine the minimum value of 2x

The minimum value of x is - 3

Therefore, the minimum value of 2x is: 2(- 3) = - 6

Step 2: Determine the maximum value of y

The maximum value of y is 3

Step 3: Calculate the smallest value of 2x - y

The smallest value of 2x - y occurs when 2x is minimized and y is maximized:

2(- 3) - 3 = - 6 - 3 = - 9

∴ The smallest value of 2x - y is - 9