The issue with using the side-splitter to solve for x is that the side-splitter theorem is used to find lengths of the sides being split by parallel lines. In this case, the x is on a line that is parallel and thus could not be solved for using this theorem.
If we created a triangle where the tops of the non-parallel lines connected, we would be able to compare the following and solve:
However, none of this would help us solve for x using this theorem.
If we created a triangle where the tops of the non-parallel lines connected, we would be able to compare the following and solve:
However, none of this would help us solve for x using this theorem.