To determine the correct inequality that represents your situation, let's analyze the given information step by step:
1. The cost of entering the fair is $7, which is a fixed amount. This means that the total cost of entering the fair, regardless of the number of rides you go on, will always be $7.
2. Each ride costs an additional $0.50. This means that for each ride you go on, you will need to spend an additional $0.50.
3. You have $20 in your pocket, and you want to ensure that you do not spend more than this amount at the fair.
Taking all this information into account, let's analyze the options provided:
A. 0.5X + 7 > 20: This inequality suggests that the total cost of entering the fair, plus the cost of the rides you go on, should be greater than $20. However, the fixed cost of entering the fair is already $7, so this inequality does not accurately represent the situation.
B. 0.5x + 7 > 20: This inequality suggests that the total cost of entering the fair ($7) plus the cost of the rides you go on (0.5x) should be greater than $20. This accurately reflects the information provided because it ensures that the total cost does not exceed $20.
C. 0.5x + 7 < 20: This inequality suggests that the total cost of entering the fair, plus the cost of the rides you go on, should be less than $20. However, this does not accurately represent the situation because the fixed cost of entering the fair is already $7.
Therefore, the inequality that most accurately models your situation is option B: 0.5x + 7 > 20.