Tutoring Transcript: How to Solve Two-Step Equations

Have you watched our video, "How to Solve Two Step Equations"? If not, here's the video:

Would you prefer to read the transcript? We understand!

Below is the transcript to our above video, How to Solve 2-Step Equations.

Important notes:

1) The transcript contains screenshots from the above video tutorial.

2) Only words/concepts not easily seen or explained by the screenshots alone have been transcribed.

3) Step one is in green, and step two is in purple for ALL problems.

To read the full transcript, please continue scrolling.

Hey, everyone! It’s Jessyka Coulter, and today I'm going to tutor you how to complete two-step equations. So, hopefully you watched my video on one-step equations, and you're ready for the next step. If you have any questions before we get started, I would highly recommend rewatching my one-step equations tutorial (https://youtu.be/dosSFnr6Zxg).

For those of you who are wondering who I am, again my name is Jessyka Coulter, and I'm the CEO and founder of Ace Cookie Tutoring. I've helped a lot of students just like you and maybe your own kiddos with math so I'd love to help you get an A in your class, and I look forward to teaching you everything you ever wanted to know about two-step equations.

Before we get started, I just want to go over a couple of reminders that I think are really important for you to understand how to do two-step equations.

The whole purpose of both one-step equations and two-step equations is to get the variable by itself; we're solving for our variable ie we're trying to figure out what the variable’s value is.

Again, I highly encourage you to rewatch the one-step equation video if you had any trouble at all with the one-step equations before moving on to two-step equations.


Now that we have those reminders out of the way, we are ready for example number one which is: 2x + 4 = 12. So, for one-step equations we had to get the variable by itself and move everything to the opposite side of the equal sign. It's the same thing here except we have two steps instead of one. The first step is in green, and the second step is in purple on my slides.

After completing the first step, we have to ask ourselves if the variable is by itself. If it is, then we are done. Yet, in Example 1, X is still attached to the 2 after step one, so we have to do another step, hence the name 2 step equations.

Before we go to example number two, I just want to take a moment and let anyone know who is looking for some one-on-one help that we are available for in-person lessons as well as lessons online through Zoom. You can do that by scheduling a lesson at www.acecookietutoring.com/book-online For some people, I know math can be really difficult, and sometimes it's just easier to have someone there next to you holding your hand and walking you through a problem step by step. If that would work better for you or for your student, we would love to work with you/your child and tutor you how to do two step equations. Again, you can book a lesson at www.acecookietutoring.com/book-online


Okay, let's go ahead and move on to example two which is: 4 – 7x = - 66. This problem is a little harder than the last example because it has negative numbers. So, the first step is to decide how to get the variable and its term on the same side of the equal sign without anything else on the same side of the equal sign. My first step is going to be minus 4 on both sides. This can be a little tricky for some of my students because they see that minus sign and don't know which term it goes to. I always tell people to look to the left of the number and/or variable to determine if it's positive or negative. In this case, there’s an invisible positive sign (+) to the left of the 4, so the four is positive.

To complete the first step, either use a number line or calculator depending on your/your child’s teacher’s requirements.

Younger kids or ones really new to negative numbers struggle with subtracting negative numbers. The way I always teach it is that you're getting more negative (the number gets bigger). Another way to think of it is: you owed someone $66, and then you asked for 4 more dollars. So, you owe the person even more money.

For step two, remember a negative number divided by a negative number is always positive ie has a positive answer.


Alright, let's go to number three which is: 6x – 10 = 8

Hopefully, you’ve seen by now step two is often division.

I hope you are enjoying this video and learning a lot about two-step equations. If you are looking for some more videos like this ie more tutorials about other subjects you might be struggling with including: English and science, check out our other tutorials at www.acecookietutoring.com/tutorial We would love to give you some free homework tips and help you out as much as we can. If you have any questions about this video or maybe there's a specific two-step problem you're working on that we didn't cover, just go ahead and leave that in the comments for us; we'd love to create another video. Thanks so much!


Now, the next example (x/2 + 3.5 = 21) might look a little scary because it has a fraction and a decimal, but I promise we're going to do this problem just like all the other two-step equations.

Step one is pretty easy; to move three point five to the other side and to get rid of it, I have to subtract both sides by 3.5.

Step two is where it gets a little tricky for some students. In order to get rid of the division sign, I have to remember the opposite of division is multiplication. So I'm going to multiply both sides by two in order to cancel out divided by 2.

If you struggled with example four, I might take a quick break and go back and re-listen to the previous slide and rework the problem on your own.

This next example is probably the hardest one in the whole presentation. I'm going to consider it the challenge example. So, depending on your age or the grade level of your student he/she might or might not be ready for this example. It is going to involve the distributive property.


Here’s the challenge example: 4 (x + 6) = 296. I'm going to go ahead and do this one on a couple different slides just in case you're not familiar with the distributive property.

The first important thing to understand here is that everything inside of the parentheses (the x plus six) is being multiplied by the 4 which is outside of the parentheses. Another way to say it: we’re going to distribute the four to the x and the positive six. A quick side note: whenever a number is directly beside parenthesis (there are no numbers or operations between a number and the parenthesis), it means multiplication. I'm gonna do 4 times X, and then I'm gonna do 4 times 6. Don’t forgot to keep track of your signs! That means I’m left with 4x + 24 = 296. Hopefully the problem now looks familiar. It’s a two step equation.

Here is how to solve the challenge example after completing the distribute property.

Before we double check our answers, I’d like to let everyone know who is interested in keeping up-to-date with us that we are on Facebook. So, if you'd like to follow us and "stay in the know"with our weekly study tips and free resources, as well as what Ace Cookie Tutoring is up to, we'd love to have you follow us. Just go to www.facebook.com/acecookietutoring to become a follower today!


To double check our answers, we're going to plug in the value we found for the variables into the original equations. If we get the same number on both sides of the equal sign, we know we did it right. You might be wondering, "Why should I double check my math answers?" The answer is simple: you want as many points as possible on every homework assignment, project, and test to get the best grade possible in the class. Double checking is a great way to make sure you did the problem correctly.


Thank you so much for listening! I hope you learned a lot about two-step equations. If you still think you could use some one-on-one help, we would love to work with you. Book a lesson at www.acecookietutoring.com/book-online

Please also know we create paid resources. So, if you would like some extra practice, we offer different activities and worksheets that we've created. We'd love to work with you on those. The link to get those paid resources is: acecookietutoring.com/shop

Finally, we do have an email list. If you'd like to get our monthly newsletter and find out what our monthly special is gonna be, we would love to have you join that list. Just send an email to acecookietutoring@gmail.com to join our email list!

Thank you so much for listening, and we look forward to talking to you in the next video!

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