Finding the values of an unknown k

[IBstudent]

Hey people...

So I have the inequality: 9-4k^2+16>0
I need to find the values for k.

So i do -4k^2>-25
4k^2<25
k^2<6.25
k<+-sqrt6.25 =+-2.5

However, since 2.5 is higher, it would be enough to state that k<2.5]

This is not right. But I can't find out were I went wrong. Please help me. I don't know what is the right answer....

I am really nervous as the exam is near and I am very confused at this fundamental concept.

Thanks in advance I would really appreciate your help guys.

 

[HallsofIvy]

Hey people...

So I have the inequality: 9-4k^2+16>0
I need to find the values for k.

So i do -4k^2>-25
4k^2<25
k^2<6.25
k<+-sqrt6.25 =+-2.5

If \(\displaystyle k^2> 6.25\) then either \(\displaystyle k> 2.5\) or \(\displaystyle k< -2.5\).

However, since 2.5 is higher, it would be enough to state that k<2.5]

This is not right. But I can't find out were I went wrong. Please help me. I don't know what is the right answer....

I am really nervous as the exam is near and I am very confused at this fundamental concept.

Thanks in advance I would really appreciate your help guys.

 

[IBstudent]

If \(\displaystyle k^2> 6.25\) then either \(\displaystyle k> 2.5\) or \(\displaystyle k< -2.5\).

Thanks for the reply. But how did you reach your answer?

Ok so K^2>6.25
K>2.5 is understood (simply sqaure root both sides

But why flip the sign at K<-2.5, isn't the rule that you only flip the sign if you multiply both sides by a negative number?

Thanks again

 

[stapel]

Ok so K^2>6.25
K>2.5 is understood (simply sqaure root both sides

What rule makes it okay to take the square root of an inequality? (Hint: There isn't one.)

Think about it this way, maybe: k^2 > 6.25, k^2 - 6.25 > 0, (k - 2.5)(k + 2.5) > 0

You can see from the factors that there must be two x-intercepts. What does your experience with graphing upward-opening parabolas tell you must be the solution interval for this quadratic inequality?