Verified Answer :

  • Evaluate the primary expression: \(1 \times 9 + 9 + 9 = 27\).
  • Calculate the value for each option: (5) results in 86, (6) in 18, (8) in 2, and (9) in 27.
  • Identify the matching value: The primary expression matches the value of option (9).
  • Final Answer: \(\boxed{(9)}\)

Explanation

  1. Evaluating the Primary Expression

We are given a series of numerical expressions and asked to compare a primary expression with several numbered options. The primary expression to evaluate is \(1 \times 9 + 9 + 9\). Following the standard order of operations (multiplication before addition), we compute:
\[1 \times 9 + 9 + 9 = 9 + 9 + 9 = 27.\]
Our task is to determine which of the numbered options yields the same result.

  1. Evaluating the Options

Now we evaluate each of the given options:

  1. Option (5): \(5 + 9(1 + 2)^2 = 5 + 9(3)^2 = 5 + 9(9) = 5 + 81 = 86\).
  2. Option (6): \(5 + 9(1) + 2^2 = 5 + 9 + 4 = 18\).
  3. Option (8): \(18 - 4^2 = 18 - 16 = 2\).
  4. Option (9): \(9 + 2(3^2) = 9 + 2(9) = 9 + 18 = 27\).
  1. Comparison and Conclusion

Comparing the result of our primary expression (\(27\)) with the results obtained for the numbered options, we see that only option (9) evaluates to \(27\). Therefore, the expression \(1 \times 9 + 9 + 9\) is equal to the expression provided in option (9). The final answer is (9).

Examples

Evaluating expressions is a fundamental skill in algebra and real-world planning. For instance, if you are planning a budget for a project where you need to buy multiple items at different prices, you would represent each item as an expression and compare the total cost to your allocated budget. Mastering these calculations ensures that your financial planning and resource allocation are accurate.

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