Let's solve the equation [tex]\(\frac{1}{2} m - \frac{3}{4} = x\)[/tex], where [tex]\(x\)[/tex] is one of the given values 20, 32, 44, or 48, to find the corresponding values of [tex]\(m\)[/tex].
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[
\frac{1}{2}m - \frac{3}{4} = x
\][/tex]
2. Isolate [tex]\(m\)[/tex]:
To isolate [tex]\(m\)[/tex], we first need to get rid of the [tex]\(\frac{3}{4}\)[/tex] term by adding [tex]\(\frac{3}{4}\)[/tex] to both sides of the equation:
[tex]\[
\frac{1}{2}m = x + \frac{3}{4}
\][/tex]
3. Solve for [tex]\(m\)[/tex]:
Now, we multiply both sides by 2 to solve for [tex]\(m\)[/tex]:
[tex]\[
m = 2 \left( x + \frac{3}{4} \right)
\][/tex]
4. Substitute each value of [tex]\(x\)[/tex]:
Let's calculate [tex]\(m\)[/tex] for each given [tex]\(x\)[/tex] value one-by-one.
- For [tex]\(x = 20\)[/tex]:
[tex]\[
m = 2 \left( 20 + \frac{3}{4} \right) = 2 \left( 20.75 \right) = 41.5
\][/tex]
- For [tex]\(x = 32\)[/tex]:
[tex]\[
m = 2 \left( 32 + \frac{3}{4} \right) = 2 \left( 32.75 \right) = 65.5
\][/tex]
- For [tex]\(x = 44\)[/tex]:
[tex]\[
m = 2 \left( 44 + \frac{3}{4} \right) = 2 \left( 44.75 \right) = 89.5
\][/tex]
- For [tex]\(x = 48\)[/tex]:
[tex]\[
m = 2 \left( 48 + \frac{3}{4} \right) = 2 \left( 48.75 \right) = 97.5
\][/tex]
### Compiled Results:
- When [tex]\(x = 20\)[/tex], [tex]\(m = 41.5\)[/tex]
- When [tex]\(x = 32\)[/tex], [tex]\(m = 65.5\)[/tex]
- When [tex]\(x = 44\)[/tex], [tex]\(m = 89.5\)[/tex]
- When [tex]\(x = 48\)[/tex], [tex]\(m = 97.5\)[/tex]
Thus, the corresponding values of [tex]\(m\)[/tex] for the given [tex]\(x\)[/tex] values are:
[tex]\([41.5, 65.5, 89.5, 97.5]\)[/tex]
