A. Divide both sides of the inequality by 6 to simplify: x/6 - 5/6 < 6
B. Divide both sides of the inequality by x to simplify: 1 - 5/x < 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
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To solve the inequality \( x - 5 < \frac{x}{6} \), the first step should be to eliminate the fraction for easier comparison.
The correct choice is:
D. Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \)
This simplifies to:
\[ 6x - 30 < x \]
So, option D is the appropriate first step in solving the inequality.
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