Considering all values of x and y for which x+y is at most 7, x is at least 2, and y is at least -1, what is the minimum value of y-2x?

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ok i think i see now thank you!

To find the minimum value of y - 2x, we need to first determine the range of x and y that satisfy the given conditions:

1. x is at least 2: This means x ≥ 2.
2. y is at least -1: This means y ≥ -1.
3. x + y is at most 7: This means x + y ≤ 7.

Combining the first and third conditions, we get:

x + y ≤ 7
x + (y - 2x) ≤ 7
-y + x ≤ 7
x - y ≥ -7 (by multiplying both sides by -1 and reversing the inequality sign)

Now, we need to find the range of values of x and y that satisfy the above condition.

Since x is at least 2, we can select any value of x greater than or equal to 2.

For simplicity, let's choose x = 2. Substituting this into the inequality, we get:

2 - y ≥ -7
-y ≥ -7 - 2
-y ≥ -9 (by simplifying)

Now, we multiply both sides of the inequality by -1 (and reverse the inequality sign) to solve for y:

y ≤ 9

So, for x = 2, the range of values for y that satisfies the conditions is y ≤ 9.

Therefore, the minimum value of y - 2x occurs when x = 2 and y = 9, and the minimum value is:

y - 2x = 9 - 2(2) = 9 - 4 = 5.

Hence, the minimum value of y - 2x is 5.