Question

which number can each term of the equation be multiplied by to eliminate the fractions before solving?
$6 - \frac{3}{4}x + \frac{1}{3} = \frac{1}{2}x + 5$
○ 2
○ 3
○ 6
○ 12

Explanation:

Step1: Identify denominators

The fractions in the equation are $\frac{3}{4}$, $\frac{1}{3}$, and $\frac{1}{2}$. Their denominators are 4, 3, and 2.

Step2: Find LCM of denominators

To eliminate fractions, we find the least common multiple (LCM) of 4, 3, and 2. Prime factorizations: 4 = 2², 3 = 3¹, 2 = 2¹. LCM is the product of highest powers: 2²×3 = 12.

Answer:

12 (corresponding to the option "12")