Answer
The inequality is valid for values between -1 and 1 (not including them) i.e. $(-1,1)$
Work Step by Step
First, we are going to set the right side to zero and factor to find the x-intercepts:
$x^2-1=0$
$(x+1)(x-1)=0$
$x_1=-1$
$x_2=1$
These are the critical points. We are going to take three values: one less than -1, one between -1 and 1, and one more than 1 to test in the original equation and check if the inequality is true or not:
First test with a value less than -1:
$(-4)^2-1<0$
$16-1<0$
$15<0 \rightarrow \text{ FALSE}$
Second test with a value between -1 and 1:
$(0)^2-1<0$
$0-1<0$
$-1<0 \rightarrow \text{ TRUE}$
Third test with a value more than 1:
$5^2-1<0$
$25-1<0$
$24<0 \rightarrow \text{ FALSE}$
These tests show that the inequality $x^2-1<0$ is valid for values between -1 and 1 (not including them) i.e. $(-1,1)$
