To eliminate the fractions in the equation [tex]\(-\frac{3}{4}m - \frac{1}{2} = 2 + \frac{1}{4}m\)[/tex], we need to find the least common multiple (LCM) of the denominators present in the equation.
Here are the steps:
1. Identify the denominators in the equation: [tex]\(4\)[/tex], [tex]\(2\)[/tex], and [tex]\(4\)[/tex].
2. Find the least common multiple of these denominators. The LCM of [tex]\(4\)[/tex] and [tex]\(2\)[/tex] (and [tex]\(4\)[/tex] again, but it is already included) is the smallest number that each of these denominators can divide into without leaving a remainder.
The LCM of [tex]\(4\)[/tex] and [tex]\(2\)[/tex] is [tex]\(4\)[/tex] because [tex]\(4\)[/tex] is the smallest number that both [tex]\(4\)[/tex] and [tex]\(2\)[/tex] divide into evenly.
Therefore, each term of the equation should be multiplied by [tex]\(4\)[/tex] to eliminate the fractions.
Hence, the correct number is [tex]\(4\)[/tex].
