Answer:
The possible values of x are, x = {4, 3, 2, 1 and 0}.
Step-by-step explanation:
According to the triangle inequality theorem, the sum of the length of any two sides of a triangle is more than the third side.
Consider the provided triangle.
Applying the triangle inequality theorem, AB + AC > BC.
Solve this inequality for x as follows:
[tex]AB+AC>BC\\8 + 12 > x +4 +2x +1\\20>3x+5\\15>3x\\5>x\\x<5[/tex]
Thus, the possible values of x are, x = {4, 3, 2, 1 and 0}.
