Main content

## Pre-algebra

### Course: Pre-algebra > Unit 7

Lesson 3: One-step addition & subtraction equations- One-step addition & subtraction equations
- One-step addition equation
- One-step addition & subtraction equations
- One-step addition & subtraction equations
- One-step addition & subtraction equations: fractions & decimals
- One-step addition & subtraction equations: fractions & decimals

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# One-step addition & subtraction equations

In this lesson, we learn how to solve simple equations with one unknown variable. To find the unknown, we remove extra numbers by doing the opposite operation on both sides of the equation. This keeps the equation balanced and helps us find the value of the unknown variable. Created by Sal Khan.

## Want to join the conversation?

- why on earth is a picture of the queen of england in this video?(106 votes)
- Hi Tianna!

Great question! I think the reason for the Queen of England is because Sal just thought "NO" to logic

Hope this helps =)(40 votes)

- How do I setup an equation like 44-q=11 It's simply a true/false answer in my pre-algebra book. The answer is simple, it's 33. However, I don't know how to setup the equation. The example in the video shows the variable minus the number equals the difference. But what about when the number is first and the variable is subtracted from the number? How can I set up this equation so that future equations that cannot simply be solved without showing work can be solved?(91 votes)
- Hey try to do this if you get 44-q=11 it you have to set it up like this at0:15he set it up like this that x+7=10. but one thing you have to remember is that if you have addition then you subtract and if you have subtraction than you have to add. in the x plus seven is equal to ten then you have to make a zero pair out of 7 so it equals to x and then you have to make the scale balance whatever you do the left side you have to on the right and subtract 10-7 which equals to 3 so you have to double like sal did in the first problem so he said this" 3+7 is indeed equal to 10.(10 votes)

- What is the Queen Elizabeth picture for?(23 votes)
- Its cause she died 2 weeks ago(3 votes)

- Why is queen elizabeth teaching me math(31 votes)
- she is the smartest(5 votes)

- Can someone please tell me why the queen is in the video? It's hilarious and it pushes me on. It's like she is saying, "Do your algebra by the order of the queen!". I'm just laughing inside.(26 votes)
- Why is the 5 considered to be a 'negative'? The way I read the equation, isn't it A, minus a positive number (n this case, 5)? And yet, Sal treats it as a negative number when balancing the equation. If it was supposed to be negative, should it not have read a - (-5) = -2?(18 votes)
- The thing with negatives, is that the dash in front of it is a minus sign. If it is a positive number, there is actually a plus sign in front of it, but we don't use it (but it's still there). This also happens with the negative. It's a minus sign.

I understand why you thought it was a positive (I thought it was positive as well before).

The equation is`a - 5 = -2`

. Treat the equation like this:`a + (-5) = -2`

. They are still the same. Again, it's one of those things that are unspoken but still there, there is an addition sign there. If it was`a - (-5) = -2`

as you stated, then it would simplify into`a + 5 = -2`

which in turn means that`a = -7`

. That was the time when my teacher taught me that the operator goes with the number or term after it. So logically, if you reordered -5 to be in front of a, you would get`-5 + a = -2`

which still gives the same answer.

Post a comment if you misunderstand something, I'll be glad to help. :-)(16 votes)

- May the queen rest in peace.

Rest In Peace Queen Elizabeth the second.😇

Also how could they be paying respects to the Queen if this was made ten years ago way before she died. Yes, I looked on youtube and it said ten years ago.(15 votes)- it was her birthday when he uploaded it to YouTube all those years ago.(20 votes)

- God save the Queen(16 votes)
- Isn't she dead?(10 votes)

- Why is Queen Elizabeth in the background for the whole video(16 votes)
- Probably paying respects(0 votes)

- I just learned that the reason he put the queen up there is because it was her birthday. Also u guys need to take a chill pill, my computer is spamming on cps because of u guys. Don't make this into instagram(16 votes)
- What is this dude talking about?(0 votes)

## Video transcript

Now that we're comfortable with the "why" of why we do something to both sides of an equation, let's see if we can apply it to some equations to solve for an unknown variable. So let's say that you have x plus seven is equal to ten, and I want to solve for x. All its saying is something plus seven is equal to ten, and you might be able to figure that out in your head, but if you want to do it a little bit more systematically, you're like well just all I want on the left hand side is an x. Well if all I want on the left hand side is an x I'd want to get rid of the seven. I want to subtract seven from the left-hand side, but if I want to maintain an equality here, whatever I do to the left-hand side I also have to do to the right-hand side going back to our scales that's so that we can keep our scale balanced, so that we can say that the left is still equal to the right. And so what we're going to be left with is x and then the sevens cancel out is equal to ten minus seven is equal to three. So that unknown is three, and you can verify it, three plus seven is indeed equal to ten. Let's try one more. Let's say we have a minus five is equal to negative two. So this is a little bit more interesting since we have all of these negative numbers here, but we can use the exact same logic. We just want an a over here on the left-hand side so we have to get rid of this negative five somehow. Well the best way of getting rid of a negative 5 is to add five to it. So I'll do that. So I will add five to the left-hand side. But if I want the left-hand side to stay equal to the right-hand side, whatever I do to the left I have to do the right. So I'm going to have to add five on the right-hand side as well, and so on the left-hand side I'm left with a, and then the negative five and the positive five cancel out and on the right hand side, and they're going to stay equal because I did the same thing to both sides, we have negative two plus five which is equal to three. So a is equal to three. Once again you can verify it. Three minus five is indeed equal to negative two.