To determine the value of [tex]\( m \)[/tex] in the equation [tex]\(\frac{1}{2} m - \frac{3}{4} n = 16\)[/tex] given that [tex]\( n = 8 \)[/tex], follow these steps:
1. Substitute the given value of [tex]\( n \)[/tex] into the equation:
[tex]\[
\frac{1}{2} m - \frac{3}{4} \cdot 8 = 16
\][/tex]
2. Simplify the equation by calculating [tex]\(\frac{3}{4} \cdot 8\)[/tex]:
[tex]\[
\frac{3}{4} \cdot 8 = 6
\][/tex]
Thus, the equation becomes:
[tex]\[
\frac{1}{2} m - 6 = 16
\][/tex]
3. Isolate the term involving [tex]\( m \)[/tex] by adding 6 to both sides of the equation:
[tex]\[
\frac{1}{2} m - 6 + 6 = 16 + 6
\][/tex]
Simplifying, we get:
[tex]\[
\frac{1}{2} m = 22
\][/tex]
4. Solve for [tex]\( m \)[/tex] by multiplying both sides of the equation by 2 to get rid of the fraction:
[tex]\[
2 \cdot \frac{1}{2} m = 22 \cdot 2
\][/tex]
Simplifying, we find:
[tex]\[
m = 44
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] is [tex]\(\boxed{44}\)[/tex].
