Solve inequation: 2^(1-x) - 2^(x+2) < 7

[SpartanDavid]

Hi.

I'm having trouble trying to solve the inequation above, and I hope you can help me a little.

I know the answer is supposed to be: x > -2 (because it's from a past exam), but I can't reach that answer.

Thanks.

 

[Steven G]

Sure someone here can help you a little or even a lot if that is what is needed.
If you read and followed the forum guidelines I am sure that you would have received help by now. The guidelines state that to receive help you must show your work so that a helper can see where you need help. So please post your attempt to solve the inequality.

 

[Dr.Peterson]

If you just need a start, I would expand the exponential terms, and eventually make a substitution like u = 2^x.

When you tell us what you have tried, you might also tell us what topics the exam covers; in that list, you may find a useful idea!

In case it matters, the solution you quote is not correct; either the problem or the answer has a small error.

 

[Steven G]

If you just need a start, I would expand the exponential terms, and eventually make a substitution like u = 2^x.

When you tell us what you have tried, you might also tell us what topics the exam covers; in that list, you may find a useful idea!

In case it matters, the solution you quote is not correct; either the problem or the answer has a small error.

Check here for the solution

 

[pka]

I'm having trouble trying to solve the inequation above, and I hope you can help me a little.
I know the answer is supposed to be: x > -2 (because it's from a past exam), but I can't reach that answer.

\(2^{1-x}-2^{x+2}<7\) now multiply by \(2^x\).
\(2-4\cdot 2^{2x}<7\cdot 2^x\)
\(4\cdot 2^{2x}+7\cdot 2^{x}-2>0\) Now introduce \(u=2^x\)

 

[lookagain]

In case it matters, the solution you quote is not correct; either the problem or the answer has a small error.

This is not true. The OP's final "supposed" answer as given to him/her, and the problem statement
as supplied, are correct.

Check here for the solution

Jomo, the link you showed was missing a plus sign where it should be "x + 2" for an exponent, so the solution on the
computer program is not correct.

\(2^{1-x}-2^{x+2}<7\) now multiply by \(2^x\).
\(2-4\cdot 2^{2x}<7\cdot 2^x\)
\(4\cdot 2^{2x}+7\cdot 2^{x}-2>0\) Now introduce \(u=2^x\)

I wanted to make sure the steps in the immediate quote box above are seen by the most recent viewers.

 

[Steven G]

Jomo, the link you showed was missing a plus sign where it should be "x + 2" for an exponent, so the solution on the
computer program is not correct.

The link has the correct problem for me and the correct solution as I worked out. Where is the problem?

 

[Dr.Peterson]

This is not true. The OP's final "supposed" answer as given to him/her, and the problem statement
as supplied, are correct.

I checked the answer by picking a number that should make the inequality true; apparently I misread something somewhere when I did that. I apologize.

 

[lookagain]

The link has the correct problem for me and the correct solution as I worked out. Where is the problem?

What I see when I click that link at the top of that page is

"2^(1-x) - 2^(x 2) < 7" \(\displaystyle \ \ \ \ \ \ \ \ \) Notice the gap in there between x and 2.


And, at the bottom of the page I see

"Real solution:
x > -1.82371"

_____________________________________________________


Why would me clicking on that link show a different result than for you or for someone else clicking on that link?

 

[Dr.Peterson]

That is definitely weird.

What I see (in Firefox) is "2^(1-x) - 2^(x+2) < 7", and the solution is "x>-2".

The link looks like "2^(1-x) + - + 2^(x+2) + < + 7", lacking the "+"'s around the "+", which could explain what you see; but it opens as "2^(1-x)+-+2^(x%2B2)+<+7", using a different mechanism for the actual "+" so that it works correctly.

It also works correctly for me in Chrome. But I strongly suspect this is some sort of browser issue.