Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?

Rationale

x ≥ 6

To solve the inequality 8,000 – 200x > 5,000 + 300x, we need to isolate x. This leads us to find that x must be greater than or equal to 6 months for the first account to have more money than the second account.

A (x ≤ 6) YOUR ANSWER

This choice incorrectly suggests that x must be less than or equal to 6 months. However, solving the inequality shows that x must be greater than or equal to 6 for the first account to exceed the second account's balance. Thus, this is not a valid solution.

B (x ≤ 30) YOUR ANSWER

This option implies that x must be less than or equal to 30 months, which does not accurately reflect the solution to the inequality. The calculation reveals that x must be at least 6, making this choice too restrictive and incorrect.

C (x ≥ 30) YOUR ANSWER

This choice states that x must be greater than or equal to 30 months, which is incorrect according to the inequality solution. The correct solution indicates that x can be 6 months or more, but there is no upper limit given in the context of the problem.

D (x ≥ 6) CORRECT

This option correctly states that x must be greater than or equal to 6 months. After solving the inequality, this is confirmed as the correct solution, indicating the minimum number of months needed for the first account to have more funds than the second.

Conclusion

The correct interpretation of the inequality 8,000 – 200x > 5,000 + 300x leads us to determine that the number of months, x, must be at least 6 for the first bank account to have more money than the second account. The options that suggest lesser or greater values than 6 do not satisfy the conditions of the inequality, confirming that x ≥ 6 is the accurate and valid solution.

x ≥ 6

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