Which of the following expressions is equivalent to 7(3x + 9) - 2(5x + 7)?
21x + 63 - 10x - 14 is equivalent to the expression 7(3x + 9) - 2(5x + 7).
To simplify the expression, we distribute the constants and combine like terms. The calculations lead to the equivalent expression of 21x + 63 - 10x - 14, confirming that choice D is correct.
This expression incorrectly simplifies the constants after distribution. Specifically, it fails to account for the correct multiplication of the terms 7(3x + 9) and 2(5x + 7), which leads to the wrong constant values of 9 and 7 instead of the correct 63 and -14.
Similar to choice A, this expression miscalculates the constants resulting from the distribution process. It incorrectly adds 10x instead of subtracting it, leading to an incorrect representation of the original expression. Additionally, the constants do not match the correct simplification.
While this choice correctly starts with 21x + 63, it incorrectly adds 14 instead of subtracting it. The proper simplification must yield a negative constant, as derived from the distribution of -2(5x + 7). This miscalculation results in an incorrect expression.
This expression accurately represents the result of distributing the terms 7(3x + 9) and -2(5x + 7). It correctly combines like terms, leading to the simplified form of 21x - 10x + 63 - 14, which is the equivalent of the original expression.
The expression 7(3x + 9) - 2(5x + 7) simplifies to 21x + 63 - 10x - 14, confirming that choice D is the correct answer. The other choices either miscalculate the constants or fail to combine like terms appropriately, highlighting the importance of careful distribution and simplification in algebraic expressions.
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