# algebra

posted by .

10^3 + 6x^2 - 90x - 54 < 0

• algebra -

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^2-9) < 0
(5x+3)(x+3)(x-3) < 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.

• algebra -

Me too but it gets counted wrong in this format.

## Similar Questions

4. ### Solve Inequality

Solve the inequality. Express your solution using interval notation and please show all of your work. x(x + 6)(8 – x) >= 0 I need help, I guess I'm not understanding the interval notation portion. I know, that when 0 <= x <= …
5. ### Math- Problem3

Solve the following inequality and write your answer using interval notation. Please show all of your work. (1 / (x+8) ) ≤ ((8-5x)/43)
6. ### Math - Problem4

Solve the inequality. Express your solution using interval notation and please show all of your work. x^4 - 7x^2 - 14 > 0
7. ### math

solve the inequality, write answer using interval notation pleas show the work 50/x+4+1<4x
8. ### algebra

Solve the following inequality and write answer using interval notation. Please show all of your work. 2x-5/3x^4-x^3+275x-125>=0
9. ### college algebra

solve the following inequality. write the answer in interval notation x^3-4x^2-21x<0 please show work so i can understand this problem better! thanks
10. ### calculus

solve the following inequality. write your solution in interval notation. x^3+9x^2-108 less than or equal to 0 please show all work

More Similar Questions