Since the triangles are similar, then the ratio of their corresponding sides are equal.
Thus,
[tex]\frac{2x-2}{3x}=\frac{8}{8+6}=\frac{8}{14}=\frac{4}{7}[/tex]
Cross-multiplying, we have:
[tex]\begin{gathered} 7(2x-2)=4(3x) \\ \Rightarrow14x-14=12x \\ \Rightarrow14x-12x=14 \\ 2x=14 \\ \Rightarrow x=\frac{14}{2}=7 \end{gathered}[/tex]
That is
x = 7
