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## Comment on

Is x Less than 0?## I'm confused about this one.

I didn't solve for x for the 2nd one but I quickly found that any negative integer replacing X would make it less that -4.

Thanks

## Hi Gabriel,

Hi Gabriel,

For statement 1, we can see that x = 0 does not satisfy the inequality 2x > 3x.

So, there's no reason to include 0 in your analysis.

For statement 2, it isn't enough to just test negative values of x.

For example, let's try a different statement 2:

(2) x + 1 < 100

If we test a bunch of negative integers they will all satisfy the inequality x + 1 < 100.

However, this does not mean that x MUST be negative.

For example, if we test x = 25 also satisfies the inequality x + 1 < 100.

----Okay, back to the question at hand---------

When we solve the inequality for x, we get: x < 1/2

This is when it's crucial to remind ourselves of the target question: Is x < 0?

This is a YES/NO question.

So, if x < 1/2, then it's possible that x = -5, in which case the answer to the target question is "YES, x IS less than 0"

It's also possible that x = 0, in which case the answer to the target question is "NO, x is NOT less than 0"

Once we have two contradictory answers to the target question, we know that the statement is not sufficient.

Does that help?

Cheers,

Brent

## Somewhat better. Need to

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