Question 827375
Let's write that whole sequence of steps properly with the correct conventions:

{{{4x=3x+9}}} ----- this part was good.

{{{x=(3x+9)/4}}} ---- you at least must show proper associate using grouping symbols, and properly.

{{{x=3}}} ---- and you found this.



Try checking that answer:
{{{4*3=3*3+9}}}
{{{12=9+9}}}
{{{12=18}}}, FALSE!
What did you do wrong?


Starting from your first good equation,
{{{4x=3x+9}}}, good as I said;
{{{4x-3x=3x+9-3x}}}, Additive Inverse of 3x,
{{{highlight(x=9)}}}, combined like terms and rule about additive inverses.
That is the answer for x.


Check: Does that answer work?
{{{4*9=3*9+9}}}
{{{36=27+9}}}
{{{36=36}}}, true.


The trouble was that you have no justification to go from
{{{4x=3x+9}}}
to
{{{x=3x+9/4}}}