Answer:
x = 40
Step-by-step explanation:
If 3 or more parallel lines are intersected by 2 or more transversals, the parallel lines divide the transversals proportionally , that is
[tex]\frac{4x}{5x}[/tex] = [tex]\frac{6x+8}{8x-10}[/tex] ( cross multiply )
4x(8x - 10) = 5x(6x + 8) ← distribute parenthesis on both sides
32x² - 40x = 30x² + 40x ( subtract 30x² from both sides )
2x² - 40x = 40x ( subtract 40x from both sides )
2x² - 80x = 0 ← in standard form ( factor out 2x from each term on the left )
2x(x - 40) = 0 ← in factored form
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x - 40 = 0 ⇒ x = 40
However , x > 0 , then x = 40
