How would you go about resolving an equation like this?

https://preview.redd.it/c7dlbv8xdkof1.jpg?width=1076&format=pjpg&auto=webp&s=1b6bc20a562ed492e8b258e704191c2a4cce1d2d

I tried solving it by doing x-2 = -x+1 and 2-x = x-2 and -2+x = -x+1 and -2+x = 1-x.

In every case I found x = 1,5 which is a solution but I feel like I didn't find all the solutions.

If I didn't find all the solutions I would like to know how to go about finding the rest and if I did find every I would like to know how we can know that is the case. Thank you for the help and I am sorry if this post violates rule 6.