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

Rationale

-2x + 14

To solve the expression 2(x + 3) - 4(x - 2), we first distribute the constants to the terms inside the parentheses and then combine like terms. This process reveals that the equivalent expression simplifies neatly to -2x + 14.

A (-2x - 2) YOUR ANSWER

This option results from incorrect calculations. After distributing and combining like terms, we obtain a positive constant instead of a negative one. The mistake likely arises from miscalculating either the distribution or the combination of terms, leading to an incorrect constant term.

B (-2x + 14) CORRECT

This expression correctly represents the simplified form of 2(x + 3) - 4(x - 2). When we distribute and simplify, we find 2x + 6 - 4x + 8, which combines to yield -2x + 14.

C (2x - 2) YOUR ANSWER

This choice incorrectly suggests a positive coefficient for x and a negative constant. The error may stem from a misunderstanding of the distribution process or an oversight during the combination of like terms, leading to incorrect signs in the final expression.

D (2x + 14) YOUR ANSWER

This option incorrectly maintains a positive coefficient for x while adding a constant of 14. The error likely arises from failing to properly account for the negative term from the second distribution, which alters the sign of the x term.

Conclusion

The expression 2(x + 3) - 4(x - 2) simplifies to -2x + 14 through careful distribution and combination of like terms. While options A, C, and D reflect various miscalculations, option B accurately captures the correct simplified form. Understanding the distribution and combining like terms correctly is crucial for achieving the right answer in algebraic expressions.

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

-2x + 14

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