Question

Solve this inequality without using Technology:

x-3/x+3 <= 5

Answer 1

Ummm... How is that possible, since you just communicated it over the internet?

Do you mean \(x - \dfrac{3}{x} + 3\) as you have written it?

Perhaps you mean \(\dfrac{x-3}{x+3}\)?

Answer 2

Yes, the second one.

Answer 3

They mean "technology" as in graphing calculators.

Answer 4

Well, then I have to chastise you a little about remembering your Order of Operations! Please add parentheses to clarify intent.

What is your plan?

Answer 5

Alright: \[(x - 3 \div x+3) \le 5 \]

Answer 6

\[\frac{ x-3 }{ x+3 } \le 5\]

Answer 7

Still no good. That's the same as you have it originally and that is not what you mean. Has to be (x-3)/(x+3) <= 5

You want to multiply by x+3, don't you? Well, be careful. It's a risky business.

Answer 8

Okay, you got it that last time.

Answer 9

Yeah, this is my first time lol

Answer 10

No worries. It takes a little practice. You're doing well.

What about that problem? Shall we multiply by x+3?

Answer 11

yeah

Answer 12

but move over the 5 to the other side

Answer 13

Warning!!!! I was trying to talk you into tripping over a dilemma. I like moving the 5, better.

If we multiply by x+3 we have a problem. Do we KNOW that x+3 is positive? No!! So, how will we know if we have to reverse the inequality or not? It's important to keep this in mind.

Okay, now we have \(\dfrac{x-3}{x+3} - 5 < 0\). What's next?

Answer 14

Alright, nvm, I got it.

Answer 15

I forgot to multiply through fully.

Answer 16

So instead of \[\frac{ -4x - 6 }{ x+3 }\] I should've got \[\frac{ -4x - 18 }{ x+3 }\]

Answer 17

Thanks anyway.

Answer 18

No worries. My goal is your success. More to do. Go get 'em.