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