To find the value of [tex]\( m \)[/tex] in the equation
[tex]\[
\frac{1}{2} m - \frac{3}{4} n = 16
\][/tex]
when [tex]\( n = 8 \)[/tex], we proceed as follows:
1. Substitute [tex]\( n = 8 \)[/tex] into the equation:
[tex]\[
\frac{1}{2} m - \frac{3}{4} \cdot 8 = 16
\][/tex]
2. Calculate [tex]\(\frac{3}{4} \cdot 8\)[/tex]:
[tex]\[
\frac{3}{4} \cdot 8 = 6
\][/tex]
So the equation now becomes:
[tex]\[
\frac{1}{2} m - 6 = 16
\][/tex]
3. Add 6 to both sides of the equation to isolate the term with [tex]\( m \)[/tex]:
[tex]\[
\frac{1}{2} m = 16 + 6
\][/tex]
[tex]\[
\frac{1}{2} m = 22
\][/tex]
4. To solve for [tex]\( m \)[/tex], multiply both sides of the equation by 2:
[tex]\[
m = 22 \times 2
\][/tex]
[tex]\[
m = 44
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] is [tex]\( 44 \)[/tex].
The correct answer is [tex]\( 44 \)[/tex].
