Question 312422
Break up the number line into 4 regions,
Region {{{1}}}: ({{{-infinity}}},{{{-6}}})
Region {{{2}}}: ({{{-6}}},{{{-4}}})
Region {{{3}}}: ({{{-4}}},{{{4}}})
Region {{{4}}}: ({{{4}}},{{{infinity}}})
Pick a point in each region (not the endpoints) and test the inequality.
If the inequality is true, that region is part of the solution set.
.
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Region {{{1}}}, let {{{x=-10}}}
 {{{ (x+6)(x-4)(x+4)>0}}}
 {{{ (-10+6)(-10-4)(-10+4)>0}}}
 {{{(-4)(-14)(-6)>0}}}
{{{-336>0}}}
False
.
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Region {{{2}}}, let {{{x=-5}}}
 {{{ (x+6)(x-4)(x+4)>0}}}
 {{{ (-5+6)(-5-4)(-5+4)>0}}}
 {{{(1)(-9)(-1)>0}}}
{{{9>0}}}
True
.
.
Region {{{3}}}, let {{{x=0}}}
 {{{ (x+6)(x-4)(x+4)>0}}}
 {{{ (0+6)(0-4)(0+4)>0}}}
 {{{(6)(-4)(4)>0}}}
{{{-96>0}}}
False
.
.
Region {{{4}}}, let {{{x=5}}}
 {{{ (x+6)(x-4)(x+4)>0}}}
 {{{ (5+6)(5-4)(5+4)>0}}}
 {{{(11)(1)(9)>0}}}
{{{99>0}}}
True
So then the solution includes Regions 2 and 4.
({{{-6}}},{{{-4}}})U({{{4}}},{{{infinity}}})