To solve the inequality \( x - 5 < \frac{x}{6} \), we want to isolate \( x \). Among the given options, the appropriate first step involves clearing the fraction.
Let's analyze the options:
A. Divide both sides of the inequality by 6 to simplify: \( \frac{x}{6} - \frac{x}{5} < 6 \) - This option is incorrect as it transforms the inequality improperly.
B. Divide both sides of the inequality by x to simplify: \( 1 - \frac{5}{x} < 6 \) - This is not a valid step unless we know \( x > 0 \), and it would complicate the inequality unnecessarily.
C. Multiply both sides of the inequality by x to simplify: \( x - 5 < 6 \) - This isn't appropriate either, as it could change the direction of the inequality based on the sign of \( x \).
D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \) - This option is a valid first step since multiplying by 6 eliminates the fraction on the right side, while preserving the inequality direction as 6 is positive.
Thus, the correct first step among the provided options is:
D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \).
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