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], follow these steps:
1. Start by substituting [tex]\( n = 8 \)[/tex] into the equation:
[tex]\[\frac{1}{2} m - \frac{3}{4} \cdot 8 = 16\][/tex]
2. Simplify the term with [tex]\( n \)[/tex] in it:
[tex]\[\frac{3}{4} \cdot 8 = \frac{3 \cdot 8}{4} = \frac{24}{4} = 6\][/tex]
3. Now, substitute back into the equation:
[tex]\[\frac{1}{2} m - 6 = 16\][/tex]
4. To isolate the [tex]\(\frac{1}{2} m\)[/tex], add 6 to both sides of the equation:
[tex]\[\frac{1}{2} m = 16 + 6\][/tex]
[tex]\[\frac{1}{2} m = 22\][/tex]
5. To solve for [tex]\( m \)[/tex], multiply both sides by 2 to get rid of the fraction:
[tex]\[m = 22 \cdot 2\][/tex]
[tex]\[m = 44\][/tex]
Therefore, the value of [tex]\( m \)[/tex] is [tex]\( 44 \)[/tex]. So, the correct answer is:
[tex]\[
\boxed{44}
\][/tex]
