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

Algebra.Com
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)   (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 > 

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 > , x > 2 must be satisfied
by x.

x >  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
RELATED QUESTIONS

The measures of the sides if an isosceles triangle are represented by x + 5, 3x + 13, and (answered by KMST)
A triangle has sides length x+4, 2x+2, and 3x-1 . If two of the angles of the triangle... (answered by richwmiller)
The sides of a triangle have lengths of 4x+6, 2x+1, and 6x-1. If the longest side is... (answered by josgarithmetic)
The perimeter of a triangle is 136. If the three sides of the triangle are (x+7), (2x-5), (answered by robertb)
The perimeter of a triangle is 136 cm. If the three sides of the triangle are (x+7) cm,... (answered by mananth)
I need help with my algebra 1. Q: the perimeter of a triangle is 136 cm. If the three (answered by richwmiller,Alan3354)
Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side (answered by solver91311)
Two sides of an equilateral triangle have lengths 2x - 2 and 3x - 6. Which could be the... (answered by richard1234)
If the side lengths for the triangle are x+3, 3x, and 2x+1, how would I use the triangle... (answered by robertb)