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anonymous
 one year ago
Need the steps to solve this inequality:
anonymous
 one year ago
Need the steps to solve this inequality:

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: we have to factorize the binomial at the left side

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1for example, at the first step, we can write: \[\Large x\left( {{x^3}  1} \right) \leqslant 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, we have to factorize x^31, do you know how to factorize it?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1ok! Then rewrite my inequality above, using your factorization

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be (x1)( x+1)( x 1)?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1not exactly, we have this: \[\Large x\left( {x  1} \right)\left( {{x^2} + x + 1} \right) \leqslant 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1since: \[\Large {x^3}  1 = \left( {x  1} \right)\left( {{x^2} + x + 1} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, we can note that \[\Large {{x^2} + x + 1}\] is always positive

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we have to study the sign of x and x1 only

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1for example, please solve this inequality: \[\Large x  1 \geqslant 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1correct! So we have this drawing: dw:1440745389311:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1a continuous line stands for positivity, whereas a dashed line stands for negativity

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we have the subsequent drawing: dw:1440745570772:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1whereas the signs +, , + indicate the sign of x^4x

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I have used the usual rule: \[\Large \begin{gathered} \left(  \right) \cdot \left(  \right) \cdot \left( + \right) = + \hfill \\ \left( + \right) \cdot \left(  \right) \cdot \left( + \right) =  \hfill \\ \left( + \right) \cdot \left( + \right) \cdot \left( + \right) = + \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so, what is your solution?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I would like to say Everything less than 1 including 1

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1you have to search for minus sign

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the solution would be [0,1]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I can see it in the lines so thank you for drawing those out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ill go over the thread a couple times to study, thank you!
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