which of the following operations could you perform on both sides of the given equation to solve it

To answer this question, we will solve the given equation.
First, we add 5:
[tex]\begin{gathered} 14x-5+5=3x+6+5, \\ 14x=3x+11. \end{gathered}[/tex]Now, we subtract 3x from the above result:
[tex]\begin{gathered} 14x-3x=3x+11-3x, \\ 11x=11. \end{gathered}[/tex]Finally, we divide by 11:
[tex]\frac{11x}{11}=\frac{11}{11}=1.[/tex]Therefore, from the given options we added 5 and subtracted 3x.
Answer: Options A and C.