Which of the following expressions is equivalent to the expression 3(a - 4) - 2(b + 8) for all values of a and b?

Rationale

3(a - 4) - 2(b + 8) simplifies to 3a - 2b - 28.

To simplify the expression, distribute the constants through the parentheses: 3(a - 4) becomes 3a - 12, and -2(b + 8) becomes -2b - 16. Combining these results gives 3a - 2b - 28, confirming that choice D is equivalent to the original expression.

A (3a - 2b + 4) YOUR ANSWER

This option incorrectly adds a constant of 4 instead of subtracting the necessary constants derived from both parts of the original expression. The correct simplification results in a negative constant, not a positive one.

B (3a - 2b - 4) YOUR ANSWER

While this option maintains the correct coefficients for a and b, it miscalculates the constant term. The simplification shows that the constant should be -28, not -4, making this choice incorrect.

C (3a - 2b - 20) YOUR ANSWER

This option again has the correct terms for a and b but inaccurately states the constant as -20. The proper simplification leads to -28, thus this choice does not represent an equivalent expression.

D (3a - 2b - 28) CORRECT

This option accurately reflects the simplified form of the original expression. After distributing and combining like terms, we find that the expression reduces correctly to 3a - 2b - 28.

Conclusion

The expression 3(a - 4) - 2(b + 8) simplifies to 3a - 2b - 28 through proper distribution and combination of terms. Choices A, B, and C miscalculate the constant term, leading to incorrect equivalents. Only choice D correctly represents the simplified expression, confirming it as the right answer.

Which of the following expressions is equivalent to the expression 3(a - 4) - 2(b + 8) for all values of a and b?

3(a - 4) - 2(b + 8) simplifies to 3a - 2b - 28.

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