Sharon has an Masters of Science in Mathematics and a Masters in Education
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 these…' 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.
'Add 7?' answered Ramon hesitantly.
'Are you asking me or telling me?' pressed the uncle.
'Telling you. You definitely add 7 to get the answer.'
'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?' asked Ramon.
'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.
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.
Uncle Martin sees Ramon is catching on. 'Now let's try a slightly harder one. If you can do this, then you will have no trouble finishing the rest of your homework.'
Martin wrote (3 + m) / 7 = 4 on the paper and asked, 'What's the first step here?' Do you know what it is? Let's see what Ramon says.
Ramon answered, 'Normally I would add or subtract the 3, but I don't know how to do that in this case.'
'See, you know more than you think! Remember, I said that the key to two-step problems is knowing the correct order to do the steps. It's usually add or subtract first, but in this case it is a lot easier to multiply first. Try the problem that way.'
Ramon wrote down some lines on the paper while talking:
'7 divided by 7 on the left just equals 1, and 7 times 4 is 28. So that leaves...'
'Now I can subtract the 3.'
'3 minus 3 is 0, and 28-3 is 25. Which means'
'I did it!'
As Ramon's uncle taught him, the two-step equation is just an equation that takes two steps to solve. If the equation is written in ax + b = c form, then it's easiest to solve it by adding or subtracting first, and saving the multiplication or division for the final step. There are some times, however, where it is easier to solve a two-step equation by doing the operations in the other order. The important thing to remember is that it will take two full steps, each completed separately. Thanks to Ramon, and of course Uncle Martin, you should understand it!
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