Difficulty: Medium

Average Score: 67%

The following list shows the first five numbers of an arithmetic sequence.
11, 14, 17, 20, 23. ...

Which of the following expressions is equivalent to 3(2x + 5) + 4x +7?

Rationale

3(2x + 5) + 4x + 7 simplifies to 10x + 22.

To simplify the expression, we first distribute the 3, yielding 6x + 15. Adding 4x and 7 gives us a total of 10x + 22, confirming that this is the correct equivalent expression.

A (6x + 12) YOUR ANSWER

This expression results from incorrectly simplifying the original equation. The distribution step is missing the addition of the constant terms correctly, as it should have included 15 from the distribution of 3(2x + 5).

B (10x + 22) CORRECT

This expression accurately reflects the simplification of the original equation. By distributing the 3, adding the like terms, and combining the constants, we arrive at the correct answer of 10x + 22.

C (10x + 12) YOUR ANSWER

This option mistakenly simplifies the constant terms. While the variable part is correct, the constant should be 22 instead of 12, indicating a miscalculation in summing the constant terms after distribution.

D (25x + 7) YOUR ANSWER

This expression incorrectly combines the terms, leading to an exaggerated coefficient for x. The distribution and addition processes were misapplied, resulting in an unrealistic outcome that does not represent the original equation.

Conclusion

The correct simplification of the expression 3(2x + 5) + 4x + 7 leads to 10x + 22. Each incorrect option reflects errors in distribution or addition, demonstrating the importance of careful arithmetic in algebraic expressions. Understanding these processes is crucial for accurately solving algebraic equations and ensuring that equivalent expressions are correctly identified.

Which of the following expressions is equivalent to 3(2x + 5) + 4x +7?

3(2x + 5) + 4x + 7 simplifies to 10x + 22.

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