Question 250978
Break up the number line into 4 regions.
{{{ x<-5}}}
{{{-5<x<-3}}}
{{{-3<x<20}}}
{{{x>20}}}
Pick a number in each region and test the inequality.
First region: {{{ x=-10}}}
{{{(-10+5)(-10-20)(-10+3)>0}}}
{{{(-5)(-30)(-7)>0}}}
{{{-1050>0}}}
False, not a valid region.
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.
Second region: {{{ x=-4}}}
{{{(-4+5)(-4-20)(-4+3)>0}}}
{{{(1)(-24)(-1)>0}}}
{{{24>0}}}
True, a valid region.
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.
Third region: {{{ x=0}}}
{{{(5)(-20)(3)>0}}}
{{{-300>0}}}
False, not a valid region.
.
.
Fourth region: {{{ x=30}}}
{{{(30+5)(30-20)(30+3)>0}}}
{{{(35)(10)(33)>0}}}
{{{11550>0 }}}
True, a valid region.
x=({{{-5}}},{{{-3}}})U({{{20}}},{{{infinity}}})