To solve the inequality \( x - 5 < \frac{x}{6} \), we want to eliminate the fraction and simplify the expression appropriately while maintaining the inequality's direction.
Let's consider the options given:
A. Divide both sides of the inequality by 6 to simplify: \( - < 6 \)
B. Divide both sides of the inequality by x to simplify: \( 1 - < 6 \)
C. Multiply both sides of the inequality by x to simplify: \( x - 5 < 6 \)
D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \)
The most effective method to eliminate the fraction while preserving the inequality is to multiply both sides by 6. Therefore, the correct first step is:
D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \).
This makes it easier to solve for \( x \).