Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 798: 12

Answer

$(-2,0)$ U $(6$, infinity)

Work Step by Step

$x*(x-6)*(x+2)>0$ $x=0$ $x-6=0$ $x=6$ $x+2=0$ $x=-2$ (-infinity, $-2)$ $(-2,0)$ $(0,6)$ $(6$, infinity) Let $x=-10$, $x=-1$, $x=1$, and $x=10$ $x=-10$ $x*(x-6)*(x+2)>0$ $-10*(-10-6)*(-10+2)>0$ $-10*-16*-8 >0$ $-1280>0$ (false) $x=-1$ $x*(x-6)*(x+2)>0$ $-1*(-1-6)*(-1+2)>0$ $-1*-7*1>0$ $7>0$ (true) $x=1$ $x*(x-6)*(x+2)>0$ $1*(1-6)*(1+2)>0$ $1*-5*3>0$ $-15 >0$ (false) $x=10$ $x*(x-6)*(x+2)>0$ $10*(10-6)*(10+2)>0$ $10*4*12>0$ $480 >0$ (true)
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