Question 309285
Break up the number line into 4 regions.
Region 1:({{{-infinity}}},{{{-11}}})
Region 2:({{{-11}}},{{{-5}}})
Region 3:({{{-5}}},{{{2}}})
Region 4:({{{2}}},{{{infinity}}})
Pick any point inside the region and test the inequality.
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Region 1: Let {{{x=-15}}}.
{{{(-4)(-17)(-10)>0}}}
{{{-680>0}}}
False.
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Region 2: Let {{{x=-8}}}.
{{{(3)(-10)(-3)>0}}}
{{{90>0}}}
True.
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Region 3: Let {{{x=0}}}.
{{{(11)(-2)(5)>0}}}
{{{-110>0}}}
False.
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Region 4: Let {{{x=3}}}.
{{{(14)(1)(8)>0}}}
{{{ 112>0 }}}
True.
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So the solution region is the union of Region 2 and Region 4.
({{{-11}}},{{{-5}}}) U ({{{2}}},{{{infinity}}})