number properties guide question in text of ch. 8 DS

[dhlee922]

hi,

there is a problem in ch. 8 of number properties that i'm having trouble solving. it is within the chapter and says:

Is x^2 <= to 2x?

1) x > 0
2) x < 3


the text goes on to solve this by plugging numbers, but is there a way to solve this algebraically?

just to be clear, i'm trying to express the question stem as:

is x squared less than or equal to 2x?

i move the 2x to the other side and set the inequality equal to 0 and then factor out an x

x(x-2) <= 0

and what i find is that both statement 1 and 2 basically tell me the same thing that x is between or equal to 0 and 2

0 <= x <= 2

is the answer that since there are infinite numbers between 0 and 2 because of non-integers, the answer is E?

i'm asking bc if i were to see this problem, i'd attack it with algebra first and was wondering how to solve this problem.

thanks

[RonPurewal]

hi,

there is a problem in ch. 8 of number properties that i'm having trouble solving. it is within the chapter and says:

Is x^2 <= to 2x?

1) x > 0
2) x < 3


the text goes on to solve this by plugging numbers, but is there a way to solve this algebraically?

just to be clear, i'm trying to express the question stem as:

is x squared less than or equal to 2x?

^^ Fine up to there.

i move the 2x to the other side and set the inequality equal to 0 and then factor out an x

x(x-2) <= 0

At this point it appears you've forgotten that this is the question. Now, it seems, you've started thinking that it's a statement.

If you are manipulating the question, ALWAYS continue to write the "?" at the end.
Otherwise, you'll do what you did here -- forget altogether that it's a question!

Is x(x - 2) < 0?

Still a question.

and what i find is that both statement 1 and 2 basically tell me the same thing that x is between or equal to 0 and 2

0 <= x <= 2

This has nothing to do with statement 1 or statement 2 at all. You're still manipulating the question.

If you replaced the current statement 1 and statement 2 with pictures of smiling baby pandas, this algebra would still be exactly the same.

Is 0 < x < 2?

is the answer that since there are infinite numbers between 0 and 2 because of non-integers, the answer is E?

No. But, now that you know what's actually the question vs. the statements, try it again. It's not that complicated; there's no need to think about integers/non-integers. Just greater than and less than.

[RonPurewal]

By the way, there are two easy ways to write "<"

1/
Underline "<".

2/
Type "less than or equal sign" into google. You'll see plenty of them in the previews on the search result page (you won't even have to click on any of the search results). Find one, copy it, and paste it.

[dhlee922]

thanks ron, i see what you mean by:

Is 0 < x < 2?

is still part of the original question stem and not to incorporate statements into the question.

that cleared everything up.

[RonPurewal]

You're welcome. Just make sure to keep that straight -- "losing the question" is a surprisingly common mistake.