The given equation is,
[tex]3(5z+1)=33[/tex]Solve for z
Divide both sides by 3
[tex]\begin{gathered} \frac{3(5z+1)}{3}=\frac{33}{3} \\ 5z+1=11 \end{gathered}[/tex]Add -1 to both sides
[tex]\begin{gathered} 5z+1-1=11-1 \\ 5z+0=10 \\ 5z=10 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5z}{5}=\frac{10}{5} \\ z=2 \end{gathered}[/tex]Therefore,
[tex]z=2[/tex]