Answer:
x = 8
Step-by-step explanation:
[tex]\sf If\:\: \overline{NO} \parallel \overline{KJ}\:\:then\:\: \triangle LNO \sim\triangle LKJ[/tex]
Therefore:
[tex]\implies \sf \overline{LN} : \overline{LO} = \overline{LK} : \overline{LJ}[/tex]
[tex]\implies (x-3):(x-4)=(x-3)+(x+2):(x-4)+x[/tex]
[tex]\implies \dfrac{x-3}{x-4}=\dfrac{2x-1}{2x-4}[/tex]
[tex]\implies (x-3)(2x-4)=(2x-1)(x-4)[/tex]
[tex]\implies 2x^2-10x+12=2x^2-9x+4[/tex]
[tex]\implies -10x+12=-9x+4[/tex]
[tex]\implies 12=x+4[/tex]
[tex]\implies x=8[/tex]
