Answer:
x=8
Step-by-step explanation:
The picture of the question in the attached figure
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
If line segment NO is parallel to segment KJ
then
Triangle LNO is similar to Triangle LKJ by AA Similarity Theorem
so
[tex]\frac{LN}{LK}=\frac{LO}{LJ}[/tex]
substitute the given values
[tex]\frac{x-3}{2x-1}=\frac{x-4}{2x-4}[/tex]
solve for x
[tex](x-3)(2x-4)=(x-4)(2x-1)[/tex]
Apply distributive property
[tex]2x^2-4x-6x+12=2x^2-x-8x+4[/tex]
Combine like terms
[tex]2x^2-10x+12=2x^2-9x+4[/tex]
[tex]10x-9x=12-4\\x=8[/tex]
