The triangle inequality requires the total length of any two sides to exceed the length of the third. This gives rise to 3 inequalities:
42 +4x > 2x -6
42 +(2x -6) > 4x
4x +(2x -6) > 42
Solve the first one by subtracting (2x +42), then dividing by 2.
2x > -48
x > -24
Solve the second one by subtracting 2x, the dividing by 2.
36 > 2x
18 > x
Solve the third by adding 6, then dividing by 6.
6x > 48
x > 8
These three inequalities must all be satisfied. Of course, all solutions to x > 8 are also solutions to x > -24. (The reverse is not true.) So, the final answer is the overlap between x > 8 and x < 18.
The possible range of x is 8 to 18.
8 < x < 18
