For example the equation $|2x-1|+3=4x$,

We can get two equations out of that, $2x-1=4x-3$ and $2x-1=-(4x-3)$. Solve the first one we get $x=1$ and for the second one $x=2/3$. But when you substitute 2/3 into the original equation, you get 10/3=8/3, which is clearly wrong. My answer sheet says the answer is rejected, but if we follow all steps correctly and get to a solution, how can it still be wrong? It's like solving $5=3+x$ and x somehow doesn't equal to two.