Answer
The inequality is valid on values between -3 and 3 (not including them) i.e. $(-3,3)$
Work Step by Step
First, we are going to set the right side to zero and factor to find the x-intercepts:
$x^2-9=0$
$(x+3)(x-3)=0$
$x_1=-3$
$x_2=3$
These are the critical points. We are going to take three values: one less than -3, one between -3 and 3, and one more than 3 to test in the original equation and check if the inequality is true or not:
First test with a value less than -3:
$(-4)^2-9<0$
$16-9<0$
$7<0 \rightarrow \text{ FALSE}$
Second test with a value between -3 and 3:
$(0)^2-9<0$
$0-9<0$
$-9<0 \rightarrow \text{ TRUE}$
Third test with a value more than 3:
$5^2-9<0$
$25-9<0$
$16<0 \rightarrow \text{ FALSE}$
These tests show that the inequality $x^2-9<0$ is valid on values between -3 and 3 (not including them) i.e. $(-3,3)$
