Question 34

10x + 22

The expression 3(2x + 5) + 4x + 7 simplifies to 10x + 22, making this option the correct choice.

A) 6x + 12

This option is incorrect because upon simplifying the expression, one would find that it does not account for the full contributions of both the 3(2x + 5) and the 4x terms. Specifically, it fails to combine the terms correctly, leading to a lower coefficient for x.

B) 10x + 22

This option is correct. When the expression 3(2x + 5) is expanded, it yields 6x + 15. Adding 4x and 7 gives 6x + 15 + 4x + 7, which simplifies to 10x + 22.

C) 10x + 12

This option is incorrect as it does not accurately reflect the constant term from the simplification process. After expanding and combining like terms, the correct constant term should be 22, not 12.

D) 25x + 7

This option is incorrect because it significantly overestimates the coefficient of x. The simplification process shows that the total coefficient of x should be 10, not 25, while the constant term also does not match the result from the original expression.

Conclusion

The correct answer, 10x + 22, accurately reflects the simplification of the given expression. All other options either miscalculate the coefficients or the constant term, demonstrating a lack of understanding of the arithmetic involved in distributing and combining like terms. Thus, option B stands out as the only valid expression equivalent to the original.