Question 42

21x + 63 - 10x - 14

The expression equivalent to 7(3x + 9) - 2(5x + 7) simplifies to 21x + 63 - 10x - 14.

A) 21x + 9 - 10x + 7

This option is incorrect because the constants have been inaccurately summed. The correct constants from the original expression are 63 and -14, which do not yield 9 + 7.

B) 21x + 9 + 10x - 7

This option is incorrect as it misrepresents the coefficients of x and the constants. The expression incorrectly adds 10x rather than subtracting 10x, and the constants do not match those derived from the original expression.

C) 21x + 63 - 10x + 14

This option is incorrect because, while it correctly identifies the linear terms, it mistakenly adds 14 instead of subtracting 14. The correct constant from the original expression should be 63 - 14, not 63 + 14.

D) 21x + 63 - 10x - 14

This option is correct as it accurately reflects the simplification of the original expression. The terms combine correctly to yield 21x from 7(3x) and -10x from -2(5x), and the constants combine correctly to give 63 - 14.

Conclusion

The correct expression, 21x + 63 - 10x - 14, accurately represents the result of simplifying the original expression. All other options either miscalculate the coefficients of x or the constants, demonstrating a failure to properly apply arithmetic operations in the context of the problem.