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:

-

<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

Answer 1

To solve the inequality \( x - 5 < \frac{x}{6} \), it's best to eliminate the fraction and isolate \( x \).

None of the options you provided correctly represent the standard first step in solving this inequality. However, the correct first step would typically involve moving all terms involving \( x \) to one side of the inequality.

To follow through with calculations:

1. Start with the original inequality:
   \[ x - 5 < \frac{x}{6} \]

2. To eliminate the fraction, you can multiply both sides of the inequality by 6 (which is the denominator in the fraction). This is generally a good step as long as you're cautious about the sign. Since 6 is positive, the inequality remains the same. Thus, you would have:
   \[ 6(x - 5) < x \]

3. Distributing the 6 gives:
   \[ 6x - 30 < x \]

After this, we can isolate \( x \).

Thus, the equivalent correct first step that matches one of your choices is:

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