SOLUTION: if the side of the triangle have measures 2x+5, 3x-2 and 6x-7. what are the possible values of x?

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Question 668378: if the side of the triangle have measures 2x+5, 3x-2 and 6x-7. what are the possible values of x?
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of any two sides of a triangle must be greater than the third side.

1.   (2x+5) + (3x-2) > 6x-7
           2x+5+3x-2 > 6x-7
                5x+3 > 6x-7
                  -x > -10
                   x < 10

2.   (2x+5) + (6x-7) > 3x-2
           2x+5+6x-7 > 3x-2
                8x-2 > 3x-2
                  5x > -4
                   x > -4%2F5

3.   (3x-2) + (6x-7) > 2x+5
           3x-2+6x-7 > 2x+5
                9x-9 > 2x+5
                  7x > 14
                   x > 2

All three inequalities x < 10, x > -4%2F5, x > 2 must be satisfied
by x.

x > -4%2F5 is automatically guaranteed by x > 2, so we can eliminate 

that one and we have x < 10 and x > 2 which can be written as

                 2 < x < 10

Edwin