What is the first step to solve the inequality x-5<x/6

Question

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

Answer 1

To solve the inequality \( x - 5 < \frac{x}{6} \), the correct first step is to eliminate the fraction.

The option that accomplishes this correctly is:

D. Multiply both sides of the inequality by 6 to simplify: \( 6x - 30 < x \).

Here’s why:

1. By multiplying both sides of the inequality by 6, you eliminate the fraction.
2. This step is valid because multiplying by a positive number (6) does not change the direction of the inequality.
3. You then simplify to get \( 6x - x < 30 \), leading you closer to isolating \( x \).

Thus, option D is the appropriate choice for the first step to solve this inequality.