How to Solve Two-Step Equations

0:01 Today, we're going to be tackling two-step algebraic equations. Hey friends, if you don't know me, I'm DJ. I've been a math teacher for over 20 years now, and I'm here to help you. So, let's jump right into it. We have 3x + 7 = 22. Now, what this is saying is 3 * some number plus 7 more gets us 22. There's a good system that you can use. It's like it's called isolating the variable. This equation is balanced. The left side here is equal to the right side. And one thing you have to remember is anything that you change on one side of the equation, you have to change on the other side of the equation just to you want to keep it balanced. What we're going to do first is we're going to subtract seven from both sides.

0:48 So from the left side and the right side. And I like to write the subtract seven right below this other one because what's really happening here is you have a positive 7 negative 7 or you're adding seven and you're taking away seven and that that creates a zero you know or it cancels out. You can think about it either way. Now since we took seven away from the left side immediately you want to take away 7 from the right side. Now the right side is 22 minus 7. So we want to take away 7 from 22. You can break up that seven into a two and a five. Take away 2 take away 5. So 22 - 7

1:33 is 15. Now we have 3 × x or 3x = 15. Now that three is attached to that x by multiplication because whenever a number is next to a letter, it means multiplication. So in order to get rid of a times three, cuz we're trying to get that x all by itself, you have to do a divided by three. And I like to show my division with a division bar here. And divided by 3. Now 3 / 3 is 1 cuz anything that has the same numerator and denominator is a 1. And now remember we just divided the left side by three. We have to divide

2:18 the right side by 3 to keep it balanced. Now the left side is x because 1 × x just gets us x and the right side is 15 / 3. and 15 divided 3 is five. So x is equal to 5. Now we always want to go back and check our work, right? So we originally had we originally had 3 x + 7 = 22. Now right here, this five is going to go right there where the x is. So let's take a look. Let's rewrite it now with with the x equaling 5. 3 × 5

3:08 + 7 = 22. Now 3 × 5 that's 15. And we have + 7 = 22. 22 = 22. Nice. That is a check. Let's move on to the next one. For this one, I'm going to move through a little bit more quickly uh because we already kind of went over how it works. So, remember, we have a left side and we have a right side. And it's super important to know that when I'm talking about left side or right side, I'm saying that um I'm saying that this right here, this equal sign right here, there's uh this is the left side and this is the right side over here. They have to stay balanced. So again, we do anything to the left

3:54 side, we have to do the same thing to the right side and vice versa. So all right. All right. No more uh no more waiting. Let's get let's get going here. All right. So 5x - 12 = 18. Remember the first thing you want to do is you want to get rid of the addition and the subtraction. So it's -2 and we want to make that a zero. So we want to do the opposite of take away 12, which is add 12. Okay? So we're going to add 12 right there. And that's a zero. And then remember we just did + 12 to the left side. Let's do + 12 to the right side. Oh man, I'm getting crazy with these colors right now. Um, okay. So 5 x. My apologies. I didn't mean to be switching up colors, but I think you guys can

4:40 follow along. And then the right side has 18 + 12, which is which is 30, right? Divided by 5. and then divide by five on both sides and you get x is equal to 6. Now you want to go back and you want to check right 5 5 * 6 - 12 = 18. Yeah, that's 30 - 12 = 18. 18 = 18. And that's what we want. Check. Awesome. All right, cool. Let's move on. Let's keep going. In this one, we have x over 4 + 9 = 15 or x / 4 + 9 = 15. All

5:29 right. So, in this problem, again, we want to get rid of the addition and subtraction. So, on the left side, we have + 9. So, let's just do subtract 9. Subtract 9. And in the previous problems, I was making that a zero. You don't need to do that actually, um, if you don't want to. I was just trying to emphasize the point that that created a zero. So, um, that those nines are going to cancel out and you're going to be left with x over 4 equals and what is 15 - 9? We can do 15 - 10, which is 5, and add one back. So, you get 6. And now we have x / 4 = 6. Now, we want

6:15 to get the x alone. So we have to get rid of that divided by four. How do we get rid of a divided by four? Well, we multiply by four. So multiply by four and that creates a one. Okay? And basically they just cancel out. And then since I multiplied the left side by four, I have to multiply the right side by four. And we are left with x equals and 6 × 4 six groups of four is 24. Here we go. 24. Nice. X is 24. And I went back and I made that a 24. 24 / 4 is 6, right? And then 6 + 9 is 15. That's a check. Check. All right, let's

7:01 keep moving on. Let's go. x / 6 - 5 = 3. What do you think is the first step in this problem? Yeah, we're going to add five to both sides. Great. Let's do that. Let's add five. Ready? Plus five plus five. Okay, so now we're going to get We just rewrite this x / 6. Don't forget those fives are going to cancel and we have eight right here. Okay, now it's x / 6. In order to get rid of a divided by six, cuz we're trying to get that x alone, you have to do the opposite. divided by 6. It's going to be time 6. All right. So 6 × then we're going to do this side. Time 6 again. Those are going to cancel and you get x equ=

7:49 48. Eight groups of six is 48. Excellent. Don't forget, go back and check your work. If this uh x was a 48, 48 / 6 is 8. 8 - 5 = 3. Yep. Check. All right, let's keep moving. 8 + 2x = 30. Now, don't worry, the 8 is on the left side now, but it's still like a it's still a plus 8, and we still have 2 × x and we have equals 30. So, on this one, you're still going to get rid of that 8. Okay? Cuz we want to do the addition and subtraction first. So, we're going to do min - 8 minus 8 and and rewrite the problem. I really like it when when you rewrite the

8:35 problem so that we don't make well we minimize mistakes is what all right 30 - 8 is 22. Nice. All right. And then we have 2 × x = 22. And again you're going to divide by 2. Divide by 2. Now I will say I get at this point that you might be saying to yourself, hey Mr. DJ, I get that 2 * some number equals 22. That number has to be 11. Yeah, you're right. I mean, you're using number sense at that point, but you also want to get in a good habit of like having a system here to check your work. So, I like to like show my work this way. Divide by two, divide by 2. X= 11, right? Again, we go back and we check our work. We put an 11 right

9:20 here. Times 2 × 11 is 22. 8 + 22 is 30. And yeah, we're good. All right, we're moving on to the last problem here. Uh, so stick with me and let's finish this up strong. In this one, we have 45 = 7x + 10. Now, again, don't get all tripped up because the uh variable x is on the right side. Um, and the + 10 is on the right side as well, and then the 45 is on the left side. It's no big deal. It all works the same way. So, we have 7 x uh 45 = 7x + 10. And what do you think we're going to do first? Yeah, right. All right, we got to get rid of that 10. So, we're going to do min - 10 - 10. Perfect. Same as every time right

10:06 now in these two-step equations. And then, uh, we have 45 - 10, which is 35 equals and now that + 10 and - 10, they just get they just get cancelled. So, we have 7 x left here. And then we have 7 * x. So, we have 7 × x. We have to do divided by 7. divided by 7 / 7 and we get 35 / 7 is 5 = x. Okay, I'm sorry that looks more like an s. 5 = x. And then let's plug it back in. We'll just double check our work. That would be a five. Ooh, that looks like 75. Put a little time symbol there. All right, so 7 × 5 is 35. 35.

10:52 Yeah, right. See 35. 35 + 10 is 45. 45 = 45. Check. All right, we tackled six two-step algebraic equations. And uh as always, thank you again and we will see you in the next video. Take care. Bye.