To solve the inequality \( x - 5 < \frac{x}{6} \), the logical first step is to eliminate the fraction for simplification.
Among the options given, the correct first step is:
D. Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \).
This transforms the inequality to: \[ 6x - 30 < x \]
This step effectively clears the fraction without changing the inequality, as long as \( 6 \) is positive.