To eliminate the fractions in the given equation:
[tex]\[
-\frac{3}{4} m - \frac{1}{2} = 2 + \frac{1}{4} m,
\][/tex]
we need to find a common multiplier that will clear all the denominators.
Let's identify the denominators in the fractions:
- For [tex]\(\frac{3}{4}\)[/tex], the denominator is 4.
- For [tex]\(\frac{1}{2}\)[/tex], the denominator is 2.
- For [tex]\(\frac{1}{4}\)[/tex], the denominator is 4.
The least common multiple (LCM) of these denominators (4, 2, and 4) is 4. Therefore, multiplying every term in the equation by 4 will eliminate the fractions.
Here’s the step-by-step solution:
1. Write the original equation:
[tex]\[
-\frac{3}{4} m - \frac{1}{2} = 2 + \frac{1}{4} m
\][/tex]
2. Identify the LCM of the denominators 4, 2, and 4. The LCM is 4.
3. Multiply every term in the equation by 4 to clear the fractions:
[tex]\[
4 \left( -\frac{3}{4} m \right) - 4 \left( -\frac{1}{2} \right) = 4 \left( 2 \right) + 4 \left( \frac{1}{4} m \right)
\][/tex]
4. Simplify each term:
[tex]\[
\left( -3m \right) - 2 = 8 + m
\][/tex]
Multiplying each term by 4 successfully eliminates the fractions. Thus, the number to multiply each term by to eliminate the fractions in the equation is:
[tex]\[
\boxed{4}
\][/tex]
