In the triangle, what is the smallest possible integer value for x? a) 6 b) 7 c) 12 d) 13

7

Explanation:
There is a theorem that states that: "In any triangle, the sum of any two sides MUST be greater that the third side."

This means that, in the given triangle:
x + 2x > 18
3x > 18
x > 18/3
x > 6

Since x should be greater than 6 for the dimensions to be valid, therefore, the smallest possible integer for x is the one directly after the 6 which is 7.

Hope this helps :)