To solve the inequality:
[tex]\[ 50 \leq \frac{m}{16} + 46 \][/tex]
we proceed with the following steps:
1. Isolate the term involving [tex]\( m \)[/tex]:
Subtract 46 from both sides of the inequality to isolate [tex]\( \frac{m}{16} \)[/tex]:
[tex]\[
50 - 46 \leq \frac{m}{16}
\][/tex]
Simplifying the left side:
[tex]\[
4 \leq \frac{m}{16}
\][/tex]
2. Solve for [tex]\( m \)[/tex]:
To eliminate the fraction, multiply both sides of the inequality by 16:
[tex]\[
4 \times 16 \leq m
\][/tex]
Performing the multiplication on the left side:
[tex]\[
64 \leq m
\][/tex]
3. Interpret the solution:
The inequality [tex]\( 64 \leq m \)[/tex] means that [tex]\( m \)[/tex] must be greater than or equal to 64. This corresponds to option C in the given choices.
Therefore, the correct answer is:
C) [tex]\( 64 \leq m \)[/tex]
