Which of the following expressions equals 3x + 5?

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To determine which expression equals (3x + 5), we can evaluate each option.

Starting with the expression in D, ((1/3)(9x + 15)), we can simplify it by distributing ((1/3)):

[ (1/3)(9x) + (1/3)(15) = 3x + 5. ]

This matches the original expression (3x + 5) perfectly, confirming that option D is indeed correct.

For the other expressions:

In option A, (3(x + 5/3)) expands to (3x + 5), when you distribute the 3, but when calculating the constant part, (3 \times 5/3 = 5), which is correct; however, it may appear misleading in its form without proper simplification.
Option B, ((3/5)(x + 5)) simplifies to ((3/5)x + 3), which does not equal (3x + 5) due to different coefficients for (x) and a mismatched constant.
In option C, (3x + 5x - 2