Final answer:
To eliminate the fractions in the given equation, each term should be multiplied by 12, which is the least common multiple of the denominators 4, 3, and 2. The correct option is D.
Step-by-step explanation:
To eliminate the fractions in the equation 6 - (3/4)x + (1/3)x = (1/2)x + 5, you need to find a common multiple of the denominators 4, 3, and 2. The least common multiple (LCM) of these numbers is 12. Therefore, by multiplying each term of the equation by 12, you will not have any fractions remaining.
This process is similar to finding the LCM in algebraic operations involving fractions. When you multiply each fraction by this number, the denominators are effectively cancelled out, simplifying the equation.
Always remember that when you are multiplying fractions, you multiply the top numbers (numerators) and keep the result over the common denominator. Here, multiplying by 12, the LCM, achieves this. The correct option is D.