SOLUTION: Please help. I got this question wrong on a test and i get to redo it. Using the Triangle Inequality Theorem, solve for all possible values of x. The sides are A=x+2, B=2x-1, and C

Question 202113: Please help. I got this question wrong on a test and i get to redo it. Using the Triangle Inequality Theorem, solve for all possible values of x. The sides are A=x+2, B=2x-1, and C=3x
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Triangle inequality theorem is, any two sides of triangle are greater than third side.
.
A=(x+2),,,,B=(2x-1),,,,,C= (3x)
.
A<(B+C),,(x+2)<(2x-1)+(3x) ,,,,x+2<5x-1,,,,3<4x,,,x>3/4
.
B<(A+C),,,(2x-1)<(x+2)+(3x),,,2x-1<4x+2,,,-3<2x,,,x>-3/2
.
C<(A+B),,,,(3x)<(x+2)+(2x-1),,, 3x<3x+1
.
From all these,,,x>3/4
.
Check,for x=3/4,,, A=(x+2)=2.75,,,,B=(2x-1)=.5,,,,C=(3x)=9/4 = 2.25
.
A3/4)
.
B .
C
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