steve816
  • steve816
Please help me solve the inequality!
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

steve816
  • steve816
\[x^3-x^2-72x >0\]
steve816
  • steve816
I solved for x and got x = 0, 9, -8 Not sure what to do from there.
jim_thompson5910
  • jim_thompson5910
so you solved x^3 - x^2 - 72x = 0 for x and you got x = 0, x = 9, x = -8 ??

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

steve816
  • steve816
Yes
jim_thompson5910
  • jim_thompson5910
ok first draw a number line and plot those three values on it |dw:1440998491371:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440998528778:dw|
jim_thompson5910
  • jim_thompson5910
label the different regions A,B,C,D |dw:1440998552769:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440998579792:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440998592421:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440998604341:dw|
steve816
  • steve816
Okay
jim_thompson5910
  • jim_thompson5910
x^3 - x^2 - 72x factors to x(x-9)(x+8) then set up a sign chart where the factors are written in a column on the left side the regions are written along the top row like this |dw:1440998659579:dw|
jim_thompson5910
  • jim_thompson5910
now let's pick a number from region A this could be any number you want as long as it's less than -8. So let's pick -9 if x = -9, then the sign of x is negative. We put a negative sign/symbol in the first row, first column like this |dw:1440998809112:dw|
jim_thompson5910
  • jim_thompson5910
keep x = -9 the same what is the value of x-9? that is x-9 = -9-9 = -18 which is also negative so place a negative symbol in the "A" column and "x-9" row |dw:1440998838462:dw|
jim_thompson5910
  • jim_thompson5910
if x = -9, then x+8 = -9+8 = -1 which is also negative |dw:1440998879510:dw|
jim_thompson5910
  • jim_thompson5910
I'm going to let y = x^3 - x^2 - 72x and write "y" in the bottom of the left most column |dw:1440998908837:dw|
jim_thompson5910
  • jim_thompson5910
to find the sign of y for column A (is y positive or negative?) we multiply the signs in column A negative*negative*negative = positive*negative = negative so ultimately, y is negative when x < -8, ie in region A |dw:1440998977212:dw|
steve816
  • steve816
So I did all the work and got x <- 8 -8 < x < 0 x > 9 Is this right?
jim_thompson5910
  • jim_thompson5910
does the sign chart make sense? if so, then go ahead and fill out the rest of it so I can see what you got
steve816
  • steve816
I figured out how to use the chart and made sense to me. So I got the answers that I wrote above.
jim_thompson5910
  • jim_thompson5910
you should have this sign chart |dw:1441000190738:dw|
jim_thompson5910
  • jim_thompson5910
take a few moments to check what I got to make sure you got the same things
jim_thompson5910
  • jim_thompson5910
did you get the same table?
steve816
  • steve816
Yup!
jim_thompson5910
  • jim_thompson5910
ok great, just checking
jim_thompson5910
  • jim_thompson5910
notice how we want to solve for x in `x^3 - x^2 - 72x > 0` which is the same as `y > 0` since I made `y=x^3 - x^2 - 72x`
jim_thompson5910
  • jim_thompson5910
look in the chart when y > 0 ie when there's a + sign in the y row |dw:1441001180490:dw|
jim_thompson5910
  • jim_thompson5910
that corresponds to the intervals `-8 < x < 0` and `x > 9` |dw:1441001210042:dw|
jim_thompson5910
  • jim_thompson5910
so the solution to `x^3 - x^2 - 72x > 0` is `-8 < x < 0` OR `x > 9` we write \[\Large (-8, 0) \cup (9, \infty)\] if we wanted to state the entire solution set in interval notation the graph confirms all this https://www.desmos.com/calculator/6qe6nf0jao
steve816
  • steve816
Wow just wow *clap clap clap* Absolutely brilliant! Thanks for your time and help man, really appreciate it.
jim_thompson5910
  • jim_thompson5910
I'm glad it's all clicking now

Looking for something else?

Not the answer you are looking for? Search for more explanations.