Ok, call it an equation or a function, it doesn't matter what it is called, the point was that the original comment is only true for the value that was used.
In the original comment we have "x = 1 + ½x" and the example used was with a cost of two (x=2) to show that the equation was true (ending in 2=2).
However if 4 is used instead (x=4) then we have ( 4 = 1 + ½[4] ) which results in an inequality (4=3) which is false.
Which is why I initially commented with a different letter on either side of the equal sign.
If you prefer to only put the value of x on the right side on the equal sign and not the left side, then a common notation for that is f(x) = 1 + ½x, which is also referred to as function notation.
So after rereading the original post (which could have been written clearer) I think your equation in your original comment is written in a way that doesn't reflect the original post.
According to the original post the right side of the equal sign is cost plus half of the cost where cost is defined as $1. So then the equation would be x = 1+ ½(1) which solves to x = 1.5.
You are correct that assigning arbitrary values is not how to solve an equation (at least by hand), but I wasn't trying to solve the equation, I was showing that the equation as written would not be true unless 2 was used.
Since the "→" notation is an alternative notation for a function, it made reading the math in your posts and the words in your posts contradictory. It would seem that you didn't read the Wikipedia link since the "→" notation is described there.