Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 798: 25

(-infinity, $3)$

$(x+2)/(x-3) < 1$ Denominator is zero when $x=3$ $(x+2)/(x-3) < 1$ $(x+2)/(x-3) = 1$ $(x+2)*(x-3)/(x-3) = 1*(x-3)$ $x+2 = x-3$ $x+5=x$ $5=0$ (false) (-infinity, $3)$ $(3$, infinity) Let $x=0$, $x=10$ $x=0$ $(x+2)/(x-3) < 1$ $(0+2)/(0-3) < 1$ $2/-3 < 1$ $-2/3 < 1$ (true) $x=10$ $(x+2)/(x-3) < 1$ $(10+2)/(10-3) < 1$ $12/7 < 1$ (false)