To solve the inequality \( x - 5 < \frac{x}{6} \), we need to choose an appropriate step to get it into a more manageable form.
Let's examine the options:
A. This suggests dividing both sides of the inequality by 6. However, that approach may complicate the expression rather than simplify it.
B. Dividing both sides by \( x \) is not advisable, especially if \( x \) can equal zero, as it would not maintain the validity of the inequality.
C. Multiplying both sides of the inequality by \( x \) will depend on whether \( x \) is positive or negative, which can lead to issues. It's not a recommended first step because it may change the direction of the inequality.
D. This suggests multiplying both sides of the inequality by 6. This is a valid approach and will help eliminate the fraction.
Thus, the first step to solve the inequality \( x - 5 < \frac{x}{6} \) is:
D. Multiply both sides of the inequality by 6 to simplify: \( 6(x - 5) < x \)
Now implementing option D allows for an easier manipulation of the terms. You would get:
\[ 6x - 30 < x \]
Which you can then proceed to solve.