Question 202113
Triangle  inequality  theorem  is,  any  two  sides  of  triangle  are  greater  than  third side.
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A=(x+2),,,,B=(2x-1),,,,,C= (3x)
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A<(B+C),,(x+2)<(2x-1)+(3x) ,,,,x+2<5x-1,,,,3<4x,,,x>3/4
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B<(A+C),,,(2x-1)<(x+2)+(3x),,,2x-1<4x+2,,,-3<2x,,,x>-3/2
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C<(A+B),,,,(3x)<(x+2)+(2x-1),,, 3x<3x+1
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From  all  these,,,x>3/4
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Check,for x=3/4,,, A=(x+2)=2.75,,,,B=(2x-1)=.5,,,,C=(3x)=9/4 = 2.25
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A<B+C,,,2.75<.5+2.25,,,2.75<2.75,,,,,just  balance,,(ok  when  x>3/4)
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B<A+C,,,.5<2.75+2.25,,,.5<5,,,ok
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C<A+B,,,,2.25<2.75+.5,,,,,2.25<3.25,,,,ok