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Find a counterexample that disproves the following statement:
(Picture Posted)

A. x = 1
B. x = -2
C. x = 100
D. x = 5

Question

I will fan, medal, and give you a testimonial! I REALLY need help!
Find a counterexample that disproves the following statement:
(Picture Posted)

A. x = 1
B. x = -2
C. x = 100
D. x = 5

anonymous · Answer

attachment

anonymous · Answer

Can someone please help?

e.mccormick · Answer

Well, what are a few values you could plug in?  And have you looked at the graph of those?

e.mccormick · Answer

Oh, and with the choices, you could just try them.

anonymous · Answer

I plugged in all the answer choices but I'm not quite sure which one it is. :(

e.mccormick · Answer

Say x=.01

$\dfrac{1}{.01}\le .01\implies $

$100\le .01 $

Which is false.  Do you see another in your list that would cause a false condition?  When you plug them in, what do you get?

anonymous · Answer

When I plugged in 1, I still get 1, so that would be false too, right?

e.mccormick · Answer

$1\le 1$ well, there is equal.  And $1=1$ so true.

e.mccormick · Answer

That is the first one, now move to the second.  Try it and what do you get?

anonymous · Answer

Oh oops, I meant true. And for the second one I got -0.5.

e.mccormick · Answer

OK.  $-.5\le -2$ is that true?

anonymous · Answer

No

e.mccormick · Answer

So there is the counter example.

anonymous · Answer

Oh okay.. Thank you for explaining it. :)

e.mccormick · Answer

To be honest, it is true $x \ge 1$ and between 0 and -1, including -1.

I'll show a graph that also shows why.

e.mccormick · Answer

https://www.desmos.com/calculator/l9rtpnywx1 See how it gets all funny between -1 and 1? That is why this happens.