Answer:
We conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.
Explanation:
Given the inequality
y > 1/2x + 2
FOR (1, 4)
y > 1/2x + 2
substituting x = 1, and y = 4
4 > 1/2(1) + 2
4 > 1/2+2
4 > 5/2
TRUE!
Reason: It is true because 4 is indeed greater than 5/2
Thus, (1, 4) satisfies the inequality.
Therefore, (1, 4) is a solution to this inequality.
FOR (-1, 1)
y > 1/2x + 2
substituting x = -1, and y = 1
1 > 1/2(-1) + 2
1 > -1/2+2
1 > 3/2
FALSE!
Reason: It is false because 1 can not be greater than 3/2
Thus, (-1, 1) DOES NOT satisfy the inequality.
FOR (2, 3)
y > 1/2x + 2
substituting x = 2, and y = 3
3 > 1/2(2) +2
3 > 1+2
3 > 3
FALSE!
Reason: It is false because 3 can not be greater than 3.
Thus, (2, 3) DOES NOT satisfy the inequality.
FOR (0, 2)
y > 1/2x + 2
substituting x = 0, and y = 2
2 > 1/2(0) +2
2 > 0+2
2 > 2
FALSE!
Reason: It is false because 2 can not be greater than 2.
Thus, (0, 2) DOES NOT satisfy the inequality.
Therefore, we conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.