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 distribute and simplify, leading us to the equivalent expression -2x + 14. This process involves combining like terms, ensuring an accurate transformation from the original expression.

A (-2x - 2) YOUR ANSWER

This choice results from incorrect simplification. While it includes the correct factor of -2x, the constant term is miscalculated. The expression fails to account for the proper distribution and combination of constants from both terms in the original equation.

B (-2x + 14) CORRECT

This is the correct answer as it accurately reflects the simplification of the expression. After distributing 2 and -4, the correct combination yields -2x as the coefficient of x and +14 as the constant term, matching the expected result.

C (2x - 2) YOUR ANSWER

This option incorrectly suggests a positive coefficient for x and an incorrect constant. The sign of the terms has been mismanaged, leading to an entirely different expression that does not align with the result of the original equation.

D (2x + 14) YOUR ANSWER

This choice erroneously presents a positive coefficient for x, which contradicts the original expression's simplification. The constant term is also miscalculated and does not represent the correct outcome after applying distribution and combining like terms.

Conclusion

To summarize, the expression 2(x + 3) - 4(x - 2) simplifies accurately to -2x + 14, confirming that understanding the distribution and combination of terms is crucial for algebraic manipulation. The other choices fail to reflect the correct simplification process, highlighting the importance of careful calculation when transforming expressions.

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

-2x + 14

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