Algebra Solve an inequality. Write as an interval

Algebra
Tutor: None Selected Time limit: 1 Day

Solve the inequality

x^3 + 5x^2 >or equal to 4x + 20

Write your answer as an interval or union of intervals.

Please note that the sign is supposed to have a line under it making it 'or equal to.'

Oct 22nd, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

x^3 + 5x^2 >or equal to 4x + 20

we can first ignore the sign and do it this way;

 x^3 + 5x^2 = 4x + 20

x^3 + 5x^2 - 4x - 20 = 0 

solve for x by factoring by grouping: 

(x^3 + 5x^2) - (4x + 20) = 0 

factor out common term 

x^2(x+5) - 4(x+5) = 0 

Factor out the (x+5) 

(x+5)(x^2-4) = 0 

the x^2-4 is a difference of two squares and thus can be factored more 

(x+5)(x+2)(x-2) = 0 

set each term to zero and solve for x 

x+5 = 0 OR x+2 = 0 OR x-2 = 0 
x = -5 OR x = -2 OR x = 2 

as interval notation: 
(-inf, -5] U [-2,2]

-2 >= x >= 2


Please let me know if you need any clarification. I'm always happy to answer your questions. Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 22nd, 2015

I typed it in exactly and it stated it as incorrect

Oct 22nd, 2015

Sorry for that dear! Let have a check on it.

Oct 22nd, 2015

(X+2)(X-2)(X+5)=0
X=-2 SOLUTION
X=2 "
X=-5 "

2<=X=>-5


Oct 22nd, 2015

are your brackets and paratheneses right?

Oct 22nd, 2015

Sure..x should be greater or equal to both 2 and -5

Oct 22nd, 2015

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