To solve the inequality y > -x + 5 for ordered pairs (x, y), you simply plug in the x-value from the ordered pair, calculate the result, and then see if the y-value of the ordered pair is greater than this result. If it is, the ordered pair is a solution to the inequality.
Let's do this for each option:
1. Option (1, 2):
Plug in x = 1 into the inequality: y > -1 + 5 = 4
Now, check the y-value of the ordered pair, which is 2: 2 is not greater than 4, so this is not a solution.
2. Option (12, 8):
Plug in x = 12 into the inequality: y > -12 + 5 = -7
Check the y-value: 8 > -7, which is true, so (12, 8) is a solution.
3. Option (11, 7):
Plug in x = 11 into the inequality: y > -11 + 5 = -6
Check the y-value: 7 > -6, which is true, so (11, 7) is a solution.
4. Option (8, 6):
Plug in x = 8 into the inequality: y > -8 + 5 = -3
Check the y-value: 6 > -3, which is true, so (8, 6) is a solution.
5. Option (4, 7):
Plug in x = 4 into the inequality: y > -4 + 5 = 1
Check the y-value: 7 > 1, which is true, so (4, 7) is a solution.
To determine which of these options is the correct answer to the original question, you would normally look for the one option that is a solution. However, here we found that options (12, 8), (11, 7), (8, 6), and (4, 7) are all solutions to the inequality y > -x + 5.
There might be a typo in the question or the multiple-choice options were not stated correctly. Multiple ordered pairs satisfy the inequality, so if the question is asking for only one correct solution, there could be an issue with the question itself. If the question is asking for all solutions that satisfy the inequality, then options (12, 8), (11, 7), (8, 6), and (4, 7) would all be correct.
