To eliminate all the fractions in the equation, we need to find the Least Common Multiple (LCM) of the denominators present in the fractions. The given equation is:
[tex]\[ 6 - \frac{3}{4} x + \frac{1}{3} = \frac{1}{2} x + 5 \][/tex]
The denominators in the equation are 4, 3, and 2.
By finding the LCM of these denominators, we can determine the number by which each term should be multiplied to eliminate the fractions.
The denominators we have are:
- 4
- 3
- 2
Now, let's find the LCM of these numbers:
- The LCM of 4 and 3 is 12 (since the smallest common multiple of 4 and 3 is 12)
- The LCM of 12 (from the previous step) and 2 is still 12 (since 12 is already a multiple of 2)
Thus, the LCM of 4, 3, and 2 is 12.
So, each term of the equation can be multiplied by 12 to eliminate the fractions.
The correct number is:
[tex]\[ \boxed{12} \][/tex]
