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

Mar 24, 2015

$2 x + 11 = 51$

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).

$2 x + 11 = 51$

$2 x + 11 - 11 = 51 - 11$

$2 x = 40$

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 $\frac{1}{2}$" )

$2 x = 40$

$\frac{2 x}{2} = \frac{40}{2}$

$x = 20$.

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.