How can you solve an equation for backtracking does not work?

Answer 1

Actually, the order of operations is precisely why you want to

subtract the 16 first.

When you are EVALUATING an expression, you do the multiplication

first, then the addition. Here, however, you are not evaluating, but

SOLVING, which really means undoing the evaluation. If I knew what x

is, I would be first dividing it by -2, and then adding 16. The

result is 32. But we want to discover what that secret number is, so

we have to work backwards. First we undo the LAST step, the

addition, to see what number I added 16 to in order to end up with

32. That number is 32 - 16 = 16. Then, we undo the FIRST step, the

division, to see what number I divided by -2 to get 16; we multiply

by -2 and find that x is -32.

So solving requires following the order of operations backward!

I often illustrate this by describing how I put on my shoes and socks.

In the morning, I put on my socks first and then my shoes, following

the order of operations for dressing. At night, I don't take off my

socks first! I first undo the last thing I did, taking off the shoes,

and then the socks. Evaluating is dressing a variable, solving is

undressing it!