Triangle Side Analysis: Solving for X when Side Lengths are 2X, X+X, and 6

To determine if this triangle has all different side lengths, we need to check whether the sides $2X$, $2X$, and $6$ are all different.

• First, note that two sides are given as $2X$. This immediately indicates these two sides are equal.
• Since $2X = 2X$, these two sides are not different, contradicting the requirement for a scalene (all sides different) triangle.
• The third side is $6$. For a triangle to be scalene, $2X$ would need to be different from $6$. However, we already have two equal sides $2X$.

Thus, irrespective of whether the third side $6$ equals $2X$ or not, the presence of two equal sides means the triangle is not scalene.

Therefore, the answer is no, it is not a triangle with different sides.

Therefore, the solution to the problem is: No.