Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Review - Page 829: 37

Answer

$(-infinity, -5] U [-2, 6]$

Work Step by Step

$(x+5)(x-6)(x+2) <=0$ $x+5=0$ $x+5-5=0-5$ $x=-5$ $x-6=0$ $x-6+6=0+6$ $x=6$ $x+2=0$ $x+2-2=0-2$ $x=-2$ Four regions to test: $(-∞, -5]$, $[-5, -2]$, $[-2, 6]$, $[6, ∞)$ Let $x=-10$, $x=-3$, $x=0$, $x=10$ $x=-10$ $(x+5)(x-6)(x+2) <=0$ $(-10+5)(-10-6)(-10+2) <=0$ $-5*-16*-8 <=0$ $-640 <=0$ (true) $x=-3$ $(x+5)(x-6)(x+2) <=0$ $(-3+5)(-3-6)(-3+2) <=0$ $2*-9*-1 <=0$ $2*9 <=0$ $18 <=0$ (false) $x=0$ $(x+5)(x-6)(x+2) <=0$ $(0+5)(0-6)(0+2) <=0$ $5*-6*2 <=0$ $-60 <=0$ (true) $x=10$ $(x+5)(x-6)(x+2) <=0$ $(10+5)(10-6)(10+2) <=0$ $15*4*12 <=0$ $720 <=0$ (false)
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