Notice that:
[tex]AB=AN+NB,[/tex]substituting AN=2x-6, AB=82, and NB=5x+4 we get:
[tex]82=2x-6+5x+4.[/tex]Adding like terms we get:
[tex]82=7x-2.[/tex]Adding 2 to the above equation we get:
[tex]\begin{gathered} 82+2=7x-2+2, \\ 84=7x\text{.} \end{gathered}[/tex]Dividing the above equation by 7 we get:
[tex]\begin{gathered} \frac{84}{7}=\frac{7x}{7}, \\ 12=x\text{.} \end{gathered}[/tex]Now, substituting x=12 in AN=2x-6 we get:
[tex]\begin{gathered} AN=2\cdot12-6, \\ AN=24-6, \\ AN=18. \end{gathered}[/tex]Finally, substituting x=12 in NB=5x+4 we get:
[tex]\begin{gathered} NB=5\cdot12+4, \\ NB=60+4, \\ NB=64. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=12, \\ AN=18, \\ NB=64. \end{gathered}[/tex]