Your final example is wrong - the implied multiplication in 2(3 - 1) has higher priority than the left-to-right rule, given the final answer as 1, not four. The simple PEMDAS / BODMAS rules are fine for grade schoolers, but they are *incomplete* and not adequate for algebra.
Your final example is wrong - the implied multiplication in 2(3 - 1) has higher priority than the left-to-right rule, given the final answer as 1, not four. The simple PEMDAS / BODMAS rules are fine for grade schoolers, but they are *incomplete* and not adequate for algebra.