Final answer:
The simplified form of the expression 3x - 4y + 1/3(6x - 12y) is 5x - 8y, which is not listed in the provided options. The closest match would be Option D if the repetition of terms is ignored.
Step-by-step explanation:
To simplify the expression 3x - 4y + 1/3(6x - 12y), you first distribute the 1/3 to the terms inside the parentheses:
- 3x - 4y + (1/3 × 6x) - (1/3 × 12y)
- 3x - 4y + 2x - 4y
Next, combine like terms, which means adding the coefficients of terms with the same variables:
- (3x + 2x) - (4y + 4y)
- 5x - 8y
The result of the expression is 5x - 8y, which is not one of the provided options. However, if the expression is intended to be exactly as written, the closest match to the simplified form is Option D, which incorrectly repeats the terms.