Question

1/(x-5)^4<0

Answer 1

Not possible. x={}

Answer 2

need to find the critical number then put on a sign chart and answer in interval notation
I need to know how to find the critical numbers, since there is no variable on top is one automatically a critical number

Answer 3

normally y you wouldn't be able to divide by zero, so:
\[x \neq 5\] but
a 4th root will never be negative(unless complex numbers) so left side will never be negative (less than zero). the condition is never satisfied (hence @c0rtez stating an empty set).

Answer 4

so it would be \[(-\infty,\infty)\]

Answer 5

That would indicate that all numbers (from -ve inf to +ve inf) satisfy the inequality. You want to say that no number satify the inequality.

Answer 6

http://hotmath.com/hotmath_help/topics/solution-sets.html

Answer 7

\[\emptyset\] 'emptyset' in the equation symbols

Answer 8

oh ok i see what you are saying thank you very much

Answer 9

oh i just looked and \[(-\infty,\infty) \] is the answer they show in the book

Answer 10

perhaps a typo in the text book and they meant '>'

Answer 11

yeah maybe because one of the math teachers wrote the book say maybe just a mistake then

Answer 12

thank you for your help though that helped a lot

Answer 13

so if that was the case then how would you solve that

Answer 14

Visually you can see that the function never becomes less than zero, from the left of the graph to the right. that indicates that there are no solutions.
http://fooplot.com/index.php?&type0=0&type1=0&type2=0&type3=0&type4=0&y0=&y1=1/%28x-5%29%5E4&y2=&y3=&y4=&r0=&r1=&r2=&r3=&r4=&px0=&px1=&px2=&px3=&px4=&py0=&py1=&py2=&py3=&py4=&smin0=0&smin1=0&smin2=0&smin3=0&smin4=0&smax0=2pi&smax1=2pi&smax2=2pi&smax3=2pi&smax4=2pi&thetamin0=0&thetamin1=0&thetamin2=0&thetamin3=0&thetamin4=0&thetamax0=2pi&thetamax1=2pi&thetamax2=2pi&thetamax3=2pi&thetamax4=2pi&ipw=0&ixmin=-5&ixmax=5&iymin=-3&iymax=3&igx=1&igy=1&igl=1&igs=0&iax=1&ila=1&xmin=-10.74&xmax=11.70524&ymin=-6.859999999999999&ymax=6.516733333333333

Answer 15

oh ok i see what you mean thank you very much, you made it very easy to understand

Answer 16

If the question was '>0' then you'd be correct in saying that the solution interval is (-inf,inf) since it is positve at every point of the graph

Answer 17

so there is really no work to show as far as solving it right?

Answer 18

right, go to that graph and change the exponent to 3, how would you answer that?

Answer 19

wouldnt it be 1/16

Answer 20

no...now your critical point comes into play. At x = 5 the denominator goes from being negative to postive and there is an undefined point! everything below this x value is negative and satifies the inequality (part of your solution set), everything above 5 is positive and is not part of your solution set. 5 itself, being undefined, is not part of the set either.

Answer 21

http://fooplot.com/index.php?&type0=0&type1=0&type2=0&type3=0&type4=0&y0=&y1=1/%28x-5%29%5E4&y2=&y3=&y4=&r0=&r1=&r2=&r3=&r4=&px0=&px1=&px2=&px3=&px4=&py0=&py1=&py2=&py3=&py4=&smin0=0&smin1=0&smin2=0&smin3=0&smin4=0&smax0=2pi&smax1=2pi&smax2=2pi&smax3=2pi&smax4=2pi&thetamin0=0&thetamin1=0&thetamin2=0&thetamin3=0&thetamin4=0&thetamax0=2pi&thetamax1=2pi&thetamax2=2pi&thetamax3=2pi&thetamax4=2pi&ipw=0&ixmin=-5&ixmax=5&iymin=-3&iymax=3&igx=1&igy=1&igl=1&igs=0&iax=1&ila=1&xmin=-10.74&xmax=11.70524&ymin=-6.859999999999999&ymax=6.516733333333333

Answer 22

wow this is so confusing

Answer 23

\[\left\{ x | x < 5 \right\}\]I didn't mean for it to confuse. I thought the last graph would better illustrate solutions.
\[1/(x-5)^3<0\]
Since the graph is negative all the way up to 5 then the solution is
\[(- \infty,5)\]
or

Answer 24

no you didnt confuse me the math confuses me lol. I have a hard time with graphs.