Final answer:
To get rid of the fractions in the equation 1/4x + 2/3 = 6, we multiply each term by the least common multiple of 4 and 3, which is 12. After the multiplication, the equation simplifies to 3x + 8 = 72, allowing us to solve for x.
Step-by-step explanation:
To eliminate the fractions in the equation 1/4x + 2/3 = 6, we need to find a number that both denominators (4 and 3) can evenly divide into, which is their least common multiple (LCM). This number would allow us to multiply each term of the equation to get rid of the fractions. In this case, the LCM of 4 and 3 is 12, as it is the smallest number that both 4 and 3 can divide evenly into without leaving a remainder.
Thus, to clear the fractions, we multiply each term of the equation by 12. Doing this step by step:
- Multiply both sides of the equation by 12: (1/4x) * 12 + (2/3) * 12 = 6 * 12
- This simplifies to: 3x + 8 = 72, as 12 divided by 4 is 3, and 12 divided by 3 is 4
Therefore, the correct choice is a) 12, which will eliminate all the fractions in the equation and allow us to solve for x.