algebra
posted by anon .
Solve the following inequality and write your answer using interval notation . Please show all your work
10^3 + 6x^2  90x  54 < 0

I think you meant
10x^3 + 6x^2  90x  54 < 0 , divide by 2
5x^3 + 3x^2  45x  27 < 0
x^2(5x+3)  9(5x+3) < 0
(5x+3)(x^29) < 0
(5x+3)(x+3)(x3) < 0
critical values are x = 5/3, 3, and 3
Test the expression for different values, one in each part of the domain.
We don't have to find the actual value, just the sign of the answer
let x = 5 , for x < 5/3
   < 0 , that works
let x = 2 , for between 5/3 and 3
 +  > 0 , no good
let x = 0 , for between 3 and 3
+ +  < 0 , that works
let x = 10, for x > 3
+++ > 0 , no good
so x < 5/3 OR 3 < x < 3
I will let you change that to the interval notation that you were taught. Personally I prefer the above notation. 
Me too but it gets counted wrong in this format.