Question

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

what is the correct option?

Answer 1

is the first option correct?

Answer 2

The correct option is to subtract x/6 from both sides of the inequality to isolate x. So the first step is to simplify the inequality as follows:

x - 5 < x/6

Multiply both sides of the inequality by 6 to eliminate the fraction:

6(x - 5) < x

Distribute 6:

6x - 30 < x

Now, subtract 6x from both sides:

-30 < x - 6x

Combine like terms:

-30 < -5x

To isolate x, divide both sides by -5. However, note that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign changes, so it becomes:

-30/-5 > x

Simplify:

6 > x

The first step is to subtract x/6 from both sides of the inequality.

Answer 3

Apologies for the misunderstanding. If the first option is to subtract x/6 from both sides of the inequality x - 5 < x/6, then that option is incorrect.

The correct first step is to subtract x from both sides of the inequality:

x - 5 < x/6

Now, subtract x from both sides:

x - x - 5 < x/6 - x

Simplifying:

-5 < -5x/6

So, the correct first step is to subtract x from both sides of the inequality.