Final answer:
The least common denominator for the equation (3/4)x + (7/9) = 2x is 36, as 36 is the least common multiple of the denominators 4 and 9.
Step-by-step explanation:
To find the least common denominator (LCD) for the equation (3/4)x + (7/9) = 2x, we must identify the smallest number that both denominators (4 and 9) can divide into without a remainder. To do this, we calculate the least common multiple (LCM) of 4 and 9.
Since the number 4 is 22 and 9 is 32, there are no common factors between them. Thus, the LCM is their product: 4 \(\times\) 9 = 36. The LCM, in this case, is the LCD for the equation, because once we have identified it, we can multiply each term in the equation by 36 to have a consistent denominator across all terms without changing the value of the equation. This step is especially useful if we need to solve the equation by combining fractions.
The correct answer is A) 36.