Question

What are the steps to solving a two-step equation `2x +11=51`?

Answer 1

`2x+11=51`

Look at the left side of the equation. Think about the order of operations.

If I picked a number for `x` what arithmetic would I do, in what order. (If it helps, pick an actual number for `x` -- one you can keep track of, like `3` or `7`, not `2` or `11`)

First I would multiply by `2`, then second, I would add `11`.

We want to undo that process. When undoing, we undo the last step first.
(Think about shoes and socks. Put them on: socks then shoes. Undo that: take off: shoes then socks.)

The opposite of adding `11` is subtracting `11`.
(It can also be described as "adding `-11`.)

We'll subtract 11 from both side (to keep the equation balanced).

`2x+11=51`

`2x+11-11=51-11`

`2x=40`

Now we can undo "multiply by `2`. Again there are two ways of describing the "undo" for that:
The opposite of multiplying by `2` is dividing by `2`.
(Or "multiplying by `1/2`" )

`2x=40`

`(2x)/2 = 40/2`

`x=20`.

As you gain experience, you'll probably skip steps when you write this. That's OK, when you're ready and still get the correct answer.