Question 338678
{{{(x+20)(x-9)(x+6)>0}}}
Break up the number line into 4 regions.
Region 1: ({{{-infinity}}},{{{-20}}})
Region 2: ({{{-20}}},{{{-6}}})
Region 3: ({{{-6}}},{{{9}}})
Region 4: ({{{9}}},{{{infinity}}})
Choose a point in each region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
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Region 1: {{{x=-21}}}
{{{(x+20)(x-9)(x+6)>0}}}
{{{(-21+20)(-21-9)(-21+6)>0}}}
{{{(-1)(-30)(-15)>0}}}
False, this region is not part of the solution.
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Region 2: {{{x=-10}}}
{{{(x+20)(x-9)(x+6)>0}}}
{{{(-10+20)(-10-9)(-10+6)>0}}}
{{{(10)(-19)(-4)>0}}}
True, this region is part of the solution.
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Region 3: {{{x=0}}}
{{{(x+20)(x-9)(x+6)>0}}}
{{{(20)(-9)(6)>0}}}
False, this region is not part of the solution.
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Region 4: {{{x=10}}}
{{{(x+20)(x-9)(x+6)>0}}}
{{{(10+20)(10-9)(10+6)>0}}}
{{{(30)(1)(16)>0}}}
Ture, this region is part of the solution.
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Solution:({{{-20}}},{{{-6}}}) U ({{{9}}},{{{infinity}}})