Question

Find the range of values of x such that each of the following inequalities is valid.

Answer 1

\((x+2)(x-1)(x+3)<0\)

Answer 2

Just to double-check whether my working and answer is correct.

Answer 3

when x=-4, (-)<0

Answer 4

when x=-2.5, (+)>0

Answer 5

when x=0, (-)<0

Answer 6

when x=2, (+)>0

Answer 7

\(\{x:x<-3~or~-2<x<1\}\)

Answer 8

Mmm ya looks great!
Using a graphing calculator is nice way to check your work:
https://www.desmos.com/calculator/9fxcgf3xqi

The polynomial dips below the x-axis exactly where we expect it to.

Answer 9

Yay!
Thank you @Zepdrix :)