we know that
the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side
so
let
a=42
b=4x
c=2x-6
case 1)
a+b> c
42+4x > 2x-6------> 4x-2x > -6-42-----> 2x > -48------> x > -24
case 2)
a+c > b
42+2x-6 > 4x------> 42-6 > 4x-2x-----> 36 > 2x-----> 18 > x----> x < 18
case 3)
b+c > a
4x+2x-6 > 42-----> 6x > 48------> x > 8
therefore
the answer is
the possible range of x is the interval (8,18)
