# Two-Step Equation: Definition & Examples

Instructor: Sharon Linde

Sharon has an Masters of Science in Mathematics and a Masters in Education

Solving problems that just have two steps can sometimes trip people up. Read on to find out what two-step equations are and see some examples. Meet our friend Ramon as he learns about this mathematical concept.

## In Need of a Whiz

Mrs. Jimenez got home from work and noticed that her son, Ramon, was looking at a book with a frown on his face. 'What's wrong, hijo?' she said.

'I missed school yesterday because I was sick, and today I was lost in math class. I don't know how I'm going to do theseā¦' Ramon briefly looked at the homework assignment, 'two-step equations.'

'Luckily it's Friday. You can ask your uncle Martin when he comes to visit tomorrow.'

Everyone knew Uncle Martin was the best at math. Let's see how his whiz skills ended up helping Ramon.

## What Is a Two-Step Equation?

The next day, Ramon's uncle came over and helped Ramon with the math homework. He said, 'Ramon, you'll see that this is very easy. A two-step equation is just a problem that takes two steps to solve. Two-step equations have more than one operation in them--like adding and multiplying or subtracting and dividing. The two-step equation is a little more complicated than the one-step equation we worked on last week.'

'I don't know about it being easy. I think the one-step equations were easy. I wish this was more of those,' replied Ramon.

'Ah, but the two-step equation is just really two of the one-step equations jumbled together. If you know how to do the one-step equation, then the two-step is just as easy,' said Martin with confidence.

'If you say so,' said a sad-looking Ramon.

Martin and Ramon went on to review. They looked at a one-step problem that asked to solve the equation x-7=10. Uncle Martin asked Ramon if he knew what to do.

'Are you asking me or telling me?' pressed the uncle.

'Good! And what is the answer?'

'I think it's 17. I'm pretty sure x is equal to 17. See, I told you the one-step problems were easy.'

But Uncle Martin pressed on, asking him to solve for 3x=9. Ramon knew how to right away.

'Divide each side by 3 and you get x equals 3,' he said.

'Perfect! Now you know almost everything you need to know to solve a two-step equation. You already know how to simplify, or make the problem easier to solve,' said Uncle Martin.

'What?! I don't know any more than I did last week,' said the skeptical Ramon. 'Wait, what's the last thing I need to know?'

Uncle Martin replied, 'The only other thing you need to know to be able to do a two-step equation is which order to do the operations.' He waited and watched his nephew before saying, 'Exactly, this is usually the exact same order I just showed you. Add or subtract first, and then multiply or divide.'

'That's it,' confirmed Martin.

So, having read the story of Ramon's dilemma and Uncle Martin's solution, did you get all that? Two-step equations have a simple strategy: Do one operation, like adding or subtracting, then the next, multiplying or dividing. Easy-peasy.

## Examples

Uncle Martin had Ramon do several two-step problems. Let's see if you can do them too. They start with this one:

2y - 5 = 13

Ramon thinks the first step is to simplify by adding 5 to each side, which changes the equation to 2y=18.

That's the adding part. The next step is to multiply or divide. In this problem, you just divide both sides by 2, which gives you y = 9.

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