27. Which of the following expressions is equivalent to 2(x + 3) - 4(x - 2)?
Answer: B
2(x + 3) - 4(x - 2) is equivalent to -2x + 14.
The expression simplifies to -2x + 14, making option B the correct choice.
A) -2x - 2
This option is incorrect because when simplifying the original expression, the result does not yield -2x - 2. The calculations show that the constant term is actually 14, not -2.
B) -2x + 14
This is the correct answer. When simplifying 2(x + 3) - 4(x - 2), we distribute and combine like terms to arrive at -2x + 14, confirming that this expression is equivalent to the original.
C) 2x - 2
Option C is incorrect as the simplification of the expression does not produce a positive coefficient for x or the constant of -2. Instead, the correct calculations yield a negative coefficient for x and a positive constant.
D) 2x + 14
This option is incorrect because it suggests a positive coefficient for x, which contradicts the established simplification of the expression. The correct result involves a negative coefficient for x.
Conclusion
The correct answer, -2x + 14, accurately reflects the simplification of the expression 2(x + 3) - 4(x - 2). All other options fail to provide the correct coefficients and constant terms derived from the original expression, thereby confirming option B as the only valid equivalent expression.