If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Course: Algebra (all content)>Unit 2

Lesson 2: Why we do the same thing to both sides of an equation

Dividing both sides of an equation

In this lesson, we learn how to find the mass of a mystery object using a balanced scale. By keeping the scale balanced and taking equal portions from both sides, we can determine the mass of the mystery object. This helps us understand the concept of equality in real-life situations. Created by Sal Khan.

Want to join the conversation?

• could you take 2x from both sides to find what x is?
• in an equation such as 1/2x=3+17 you could turn it into x=6+34 if that's what you mean
• why is a balance there
• to show how an equation works with the example of an old fashioned scale.
If you keep the scale balanced, the equation is correct, but if one side is heavier than the other side, you would not have a true equation.
• why didn't you do it the old fashion way 3x=9 and solve by doing in inverse opperation
• because he want us to learn the concept.
• At he says that 1/3 of this total mass is equal to 1/3 of that total mass. If the unknown mass was 5x and not 3x would you have to multiply by 1/5? Or if it was 8x would you have to multiply by 1/8?
• Yes, or instead you could divide by 5 or 8. In fact the division sign came from fractions...
• Cant you just count and see there are 9 kilograms on one side and divide the 9 by the number of mystery weights and get 3 ?
• can we use other letter than x in mathematics
• yes we could, but x is more commonly used.
• what i do is basically 3x=9 /3 on both sides
• how to solve quardratic formula
• If you have an equation that looks like, "x^2+2x+1", you can either factor it out or use the quadratic formula to solve. If you want to use the quadratic formula, a = 1 (because there is 1 x^2), b =2 (since there are 2 x's), and c = 1 (since it is 1). All you have to do is plug those into the quadratic formula and simplify.
(1 vote)
• In the video he named different ways to solve this problems, does anybody have any other ways to solve it? or there is only one way to solve it
• there is usually more than one way to solve a problem.
• Yes, you can. Multiplying something by a fraction is the same as dividing by its reciprocal (ie: 1/3 and 3) and vice versa. For example: 2 multiplied by 1/3 =?

2/1*1/3=2/3

OR

2 divided by 3 =
2/3
• great 9 :3 = 3
(1 vote)

Video transcript

So we have our scale again. And we've got some masses on the left hand side and some masses on the right hand side. And we see that our scale is balanced. We have the same total mass on the left hand side that we have on the right hand side. Instead of labeling the mystery masses as question mark, I've labeled them all x. And since they all have an x on it, we know that each of these have the same mass. But what I'm curious about is, what is that mass? What is the mass of each of these mystery masses, I guess we could say? And so I'll let think about that for a second. How would you figure out what this x value actually is? How many kilograms is the mass of each of these things? What could you do to either one or both sides of this scale? I'll give you a few seconds to think about that. So you might be tempted to say, well if I could end up with just one mystery mass on the left hand side, and if I keep my scale balanced, then that thing's going to be equal to whatever I have on the right hand side. And that part would actually be a true statement. But then to get only one of these mystery masses on the left hand side, you might say, well why don't I just remove two of them? You might just say, well why don't I just remove-- let me do it a good color for removing-- why don't I just remove that one and that one? And then I'll just be left with that right over there. But if you just removed these two, then the left hand side is going to become lighter or it's going to have a lower mass than the right hand side. So it's going to move up and the right hand side is going to move down. And then you might say, OK, I understand. Whatever I have to do to the left hand side, I have to do to the right hand side in order to keep my scale balanced. So you might say, well why don't I remove two of these mystery masses from the right hand side? But that's a problem too because you don't know what this mystery mass is. You could try to remove two from this, but how many of these blocks represent a mystery mass? We actually don't know. But you might then say, well let's see, I've got three of these things here. If I essentially multiply what I have here by 1/3 or if I only leave a 1/3 of the stuff here, and if I only leave a 1/3 of the stuff here, then the scale should be balanced. If this has the total mass as this, then 1/3 of this total mass is going to be the same thing as 1/3 of that total mass. So let's just keep only 1/3 of this here. So that's the equivalent to multiplying by 1/3. So if we're only going to keep 1/3 there, we're going to be left with only one of the masses. And if we only keep 1/3 here, let's see, we have one, two, three, four, five, six, seven, eight, nine masses. If we multiply this by 1/3, or if we only keep 1/3 of it there, 1/3 times 9 is 3. So we're going to remove these . And so we have 1/3 of what we originally had on the right hand side and 1/3 of what we originally had on the left hand side. And they will be balanced because we took 1/3 of the same total masses. And so what you're left with is just one of these mystery masses, this x thing right over here, whatever x might be. And you have three kilograms on the right hand side. And so you can make the conclusion, and the whole time you kept this thing balanced, that x is equal to 3.