Solving the inequality for x, which statement shows a good first step and which is the correct solution?

Question

x−6<x4
(2 points)

Answer 1

A good first step would be to add 6 to both sides of the inequality:

x - 6 + 6 < x + 4

This simplifies to:

x < x + 10

However, this inequality does not have a single, specific solution for x. It is not possible to isolate x on one side of the inequality. Thus, the correct solution cannot be determined.

Answer 2

first step and which is the correct solution?

x−6<x4
(2 points)

1. Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
2.Divide both sides of the inequality by 4 to simplify: x4−32<x
3.Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
4.Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4

Answer 3

The correct first step would be to add 6 to both sides of the inequality:

x - 6 + 6 < x + 4

Simplifying this gives:

x < x + 10

However, it is not possible to isolate x on one side of the inequality in order to find a specific solution.

Answer 4

Thats incorrect just choose one of the options

Answer 5

Apologies for the confusion. The correct first step is:

1. Divide both sides of the inequality by x to simplify: 1−6x<4

The correct solution is:

x < 6

Answer 6

Thanks thats all you had to say the first time

Answer 7

Apologies for the confusion in my initial response. Thank you for bringing it to my attention. I appreciate your understanding.

Answer 8

Thats all wrong too.
The correct answer is : Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x

Answer 9

I apologize for my previous incorrect response. You are correct.

The correct first step is to multiply both sides by 4 to clear the inequality of fractions:

(4x - 24) < 4

The correct solution is:

4x - 24 < x

Adding 24 to both sides:

4x < x + 24

Subtracting x from both sides:

3x < 24

Dividing both sides by 3:

x < 8

Thank you for correcting me, and I apologize for any confusion caused.