Thanks to the Triangle Proportionality Theorem, we know that the division the line creates divides the sections proportionally. Thus, we can use ratios to help solve this problem.
[tex] \frac{6}{30} = \frac{3x - 2}{50} [/tex]
Multiply both sides by 50.
[tex]\frac{300}{30} = 3x - 2[/tex]
Simplify the left side.
[tex]10 = 3x - 2[/tex]
Add 2 to both sides.
[tex]12 = 3x[/tex]
Divide both sides by 3.
[tex]4 = x[/tex]
Therefore, x is equal to 4.
