Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 30

$(-5, 5)$

$x^2<25$ $x^2-25<25-25$ $x^2-25 < 0$ $(x-5)(x+5) <0$ $x-5=0$ $x=5$ $x+5=0$ $x=-5$ (-infinity, $-5)$ $(-5, 5)$ $(5$, infinity) Let $x=-10$, $x=0$, $x=10$ $x=-10$ $x^2<25$ $(-10)^2<25$ $100 < 25$ (false) $x=0$ $x^2<25$ $0^2<25$ $0 < 25$ (true) $x=10$ $x^2<25$ $10^2<25$ $100 < 25$ (false)