Answer
The inequality is valid only between the values of -2 and 5 (not including them) i.e. $(-2,5)$
Work Step by Step
First, we are going to set the right side to zero and factor to find the x-intercepts:
$x^2-3x-10$
$(x-5)(x+2)$
$x_1=-2$
$x_2=5$
These are the critical points. We are going to take three values less than -2, between -2 and 5, and more than 5 to test in the original equation and check if the inequality is true or not:
First test with a value less than -2:
$(-3)^2-3(-3)-10<0$
$9+9-10<0$
$8<0 \rightarrow \text{ FALSE}$
Second test with a value between -2 and 5:
$(0)^2-3(0)-10<0$
$9-9-10<0$
$-10<0 \rightarrow \text{ TRUE}$
Third test with a value more than 5:
$(6)^2-3(6)-10<0$
$36-18-10<0$
$8<0 \rightarrow \text{ FALSE}$
These tests show that the inequality $x^2-3x-10<0$ is valid only between the values of -2 and 5 (not including them) i.e. $(-2,5)$
