We would have to solve the equation
![9(2x+(1)/(3))=39](https://img.qammunity.org/2023/formulas/mathematics/high-school/mkp62jtm1ui48el4cbl0vj0n68vrj6uufn.png)
Step by step to determine if Timothy made a mistake.
Step 1
Expand the bracket
![\begin{gathered} (9*2x)\text{ +(9}*(1)/(3))=39 \\ 18x+3\text{ = 39} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/38o1c2ll4808i5fjlkv6e3khxz30lu0uhd.png)
Hence, his step 1 is correct.
Step 2
Bring like terms together
![\begin{gathered} 18x=39-3 \\ 18x=36 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/y7j3fi5k0ngyyv7ygqzbi1k9du2fctd3a9.png)
Step 3
Simplify step 2 and find the value of x
![\begin{gathered} (18x)/(18)=(36)/(18) \\ x=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/15rdi4tx6zn56nqeejfgsxmuhbaycv2pdg.png)
Hence, from all the steps through 1 to 3, we can conclude that Timothy did not make a mistake. Hence the right answer is option D