Posted by Austin on .
name the integer values of x that form a triangle with 12x, 12, 12+x

Geometry 
MathMate,
Any side of a triangle must be positive:
12x>0
x<12
The sum of any two sides must be greater than the third. In this case,
12x + 12 > 12+x
=>
24x > 12 + x
=>
x < 6
Also,
12+12+x > 12x
2x>12
x>6
Therefore the conditions are that
6<x<6