Question

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Answer 1

I think a better response from me (different from checking your answer) would be encouraging you to learn how to check your own answer(s).

You want to know whether your answer (which is a set of x-values) is correct or not? Then please choose a couple of test numbers from within that set and substitute them into the original inequality. If the inequality is TRUE for all the test numbers you tried, then your answer (set of x values) is very likely correct. Otherwise, it's back to the drawing board!

Answer 2

What a darling kitty! Is she for sale? :)

Answer 3

I want that kitty. I want that kitty. I want that kitty.

Supposing you've checked your own work and are still not certain you're right...if you'd show me what you'd done so far, I'd be happy to respond. Wow. It's good that you understand your personality as well as you do. Back off...expect good things from yourself, your best, but don't be harsh with yourself!

Answer 4

So, what are your conclusions about the correctness of your own work?

Answer 5

I conclude that x=2 is not a solution of either of the given inequalities.

This may make the work of checking your answer a bit easier:

Multiply (2/3)x>8 by 3 to remove the fractional coefficient.

Then 2x>24, or x>12.

I believe you've obtained that yourself.

Now you've chosen x=2 as a test point. (Note that this value of x is NOT part of y our proposed solution set.) Is 2>12 true or false?

Now choose an x value that IS a part of your solution set. For example, choose x=13 (which is larger than 12) or x=-5 (which is smaller than 6).

Answer 6

If x=13, is x>13 true or false?

If x = -5, is x<6 true or false?

If I were you I'd choose test numbers primarily from what I thought are the solution sets. Thus, I wouldn't choose x=2 (although it won't hurt to use x=2).

Answer 7

That's a great plan. If you do that consistently, you'll likely be far ahead of the crowd who do not bother to take notes. All the best to you! (Reminder: I want that kitty.)