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## Algebra (all content)

### Unit 2: Lesson 2

Why we do the same thing to both sides of an equation# Representing a relationship with an equation

Equations are about relationships (no, not girlfriends and boyfriends!) between the two sides of the equation. Let's again use a scale example to help us understand. Created by Sal Khan.

## Want to join the conversation?

- Why is learning geometry so important if all we need is algebra to prosper?(8 votes)
- Algebra is another branch of mathematics(3 votes)

- How do you find the balance if the right side doesn't have an 1 kg and a unknown kg like in the video. Or in simpler terms what can you do when you can't simply cross out the same units?(6 votes)
- Then you have to add some sort of mass (either 1kg's or unknowns) to both sides to isolate the unknown on the left side. If you have x+2=0 you will subtract 2 from both sides and you get x=-2. In algebra, the unknown can be negative, and either side of the equation can be negative as well. So x=-2 is completely ok. However it's not ok to say in word problems that you have a mass of -2kg.See?(3 votes)

- How do you find the equation for this relation:

{(1,2), (2,9), (3,28), (4,65), (5,126)}(5 votes)- Hello, I'm glad that I can solve your problem.

For lower grade students, it really can be a problem.

Since 1^3=1, 2^3=8,3^3=27,4^3=64,5^3=125，（x^3 means x*x*x）

We will get y=x^3+1 in this question. (x,x^3+1)

I hope this will help you a lot.(3 votes)

- What is a mathematical relationship? (I will look, but first jotting it here)(3 votes)
- The word relationship means "how items are connected". The same definition applies in math. A relationship shows how numbers or variables are connected. For example, an equation where the value of one variable determines (calculates) the value of another variable is a relationship.(4 votes)

- If he used a symbol to represent the unknown number like x.Will the other mass must be known as another symbol to make make sense or not. I would like a fully detailed answer to this.(2 votes)
- You can obviously represent the unknown with a variable of your choice.

But in the above case , sal represented the unknown with a question mark just to make it clear that its an unknown .

Here , we knew the mass of the right side so that is why we didn't represented it by any variable . We were asked to find the mass of that unknown ( question mark ) on the left side .

And if we would have also represented the other know mass with a variable , then we would need atleast two equations to solve for the 2 unknown variables .

Hope this clears your doubt !!(4 votes)

- Can you use an X instead of a question mark?(2 votes)
- Yes! You can use anything, even a silly doodle, to represent an unknown.(6 votes)

- So, whatever you do to the right hand side, you have to do the same to the left?(3 votes)
- Yes. Otherwise the "equation" will no longer remain "equal".

Just think: if we have 5=2+3, and someone says, "I don't like the number 2 because it is an even number, so I'm going to remove it from the equation," erases it, and says, "Now there are only odd numbers in the equation, and I like it very much." Unfortunately, the "equation" will become 5=3. 5 of course does not equal 3. Since 2 was subtracted from the right hand side, 2 must also be subtracted from the left.(3 votes)

- is algebra the same thing as math or a type of math what is the catagory of algebra(2 votes)
- Math is a very broad topic, just like history is very braod. Algebra is just one are of math. You start by learning basic math, then pre-algebra, then algebra, geometry, trigonometry, calculus and other math subject areas.(4 votes)

- why is he using a question mark instead of a variable?(2 votes)
- He is doing that to show the idea that is behind a variable. The convention to represent a variable is to use a letter, however it could be any kind of symbol that we know. Thus, he is doing that to emphasize that, and also to make beginner students more comfortable with the idea of a variable, which is very important to the study of algebra. Another reason is that he is using it to represent an unknown value. Hope this helps.(4 votes)

- Do you have to use kilograms?(2 votes)

## Video transcript

I now want to refigure out
what this mystery mass is, but we're going to start using a
little bit more of mathematics. And mathematics really
are just a language, symbols for representing ideas,
for representing relationships between things. And so the first
thing I want you to do is think about if you can
express a relationship mathematically between
this side of the scale and that side of the scale. And I'll give you some hints. We know that they
have equal mass. So maybe you can
set up some type of relationship using an
equal sign, somehow showing that this right over
here is equal to that. And I'll give you a
few seconds to do that. So let's think about
it a little bit. What do we have on this side? Well, we have our mystery mass. And I'll represent
that mystery mass by the question mark
right over here. But that's not the
only thing that we have on the left-hand side. We also have these
other 3 kilograms. So let me write over here. We'll assume that we're
dealing with kilograms. So we have the mystery
mass in kilograms plus 3 more kilograms. That's what we have here
on the left-hand side. Now, what do we have here
on the right-hand side? Well, we just have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 kilograms. So we just have 10. We just have 10 on
the right-hand side. And what else do we know? Well, we know that this scale
is balanced, that the mass here is equal to the mass here. Because the scale is balanced
the way it's been drawn, we know that these
two things are equal. So we have just
set up an equation. We're using question
mark as our unknown. We don't know what
this mystery mass is. If we add 3 kilograms
to it, then we see that it has the exact
same mass as 10 kilograms. Now my question to you is,
what can we do to this equation so that we can essentially
solve for the unknown, so that we can figure
out what the unknown is? Well, we saw in the
last little problem that we had that if we wanted
to figure out this mystery mass, we had to remove 3
kilograms from both sides. If we just removed 3
kilograms from one side, then the scale wouldn't
be balanced anymore. And we really wouldn't be able
to say that the mystery mass is equal to the thing on the right. In order to say they're
equal, the stuff has to actually be balanced. So in the last video,
we removed 3 of these. We removed 3 kilograms
from both sides in order to keep
the scale balanced. So mathematically, we'll do
the exact same thing over here. We will remove 3,
not from one side. If we remove 3 from
one side, then it wouldn't be equal anymore. We need to remove
3 from both sides. So we need to remove 3. We need to subtract 3 from
both sides of this equation in order to keep
the scale balanced. So on the left-hand side,
what are we left with? Well, just like over here, we're
left with just the question mark. 3 minus 3 is 0. So on the left-hand side, we're
left with just the question mark. And on the right-hand side,
we're left with 10 minus 3, which is 7. And we get the
exact same result. Question mark is equal to 7. And if we're dealing
with kilograms, then this is 7 kilograms.