Final answer:
To clear fractions in the equation 1/4x + 2/3 = 6, one must multiply each term by 12, which is the least common multiple of the denominators 4 and 3.
Step-by-step explanation:
To clear the fractions in the equation 1/4x + 2/3 = 6, you need to find a common multiple of the denominators 4 and 3. The smallest common multiple of 4 and 3 is 12. Therefore, to eliminate the fractions, you multiply each term of the equation by 12. This strategy ensures you will not end up with any fractions and can work with whole numbers instead.
The equation becomes:
(12)(1/4)x + (12)(2/3) = (12)(6)
Which simplifies to:
3x + 8 = 72
Consequently, the correct answer is to multiply by 12 to clear the fractions.