In order for those lines to be parallel, the two labeled angles need to add to 180°. (When discussing parallel lines, those two angles are often referred to as "same-side exterior angles" and they are "supplementary" angles...they add to 180.) Once you know that information, you just need to set up and solve the following equation:
[tex](5x+9)+(3x+11)=180[/tex]
Combining like terms, we get:
[tex]8x+20=180[/tex]
Subtracting 20 from each side, we get:
[tex]8x=160[/tex]
Dividing each side by 8, we get:
[tex]x=20[/tex]
That's the value of x. We can check our work by substituting 20 into the original equation to ensure it checks out:
[tex](5(20)+9)+(3(20)+11)=180[/tex]
[tex](100+9)+(60+11)=180[/tex]
[tex](109)+(71)=180[/tex]
[tex]180=180[/tex]
Checks out! [tex]x=20[/tex] is the solution!
