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.

## 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?
• Algebra is another branch of mathematics
• 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?
• 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?
• How do you find the equation for this relation:
{(1,2), (2,9), (3,28), (4,65), (5,126)}
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)
• What is a mathematical relationship? (I will look, but first jotting it here)
• 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.
• 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.
• 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 !!
• Can you use an X instead of a question mark?
• Yes! You can use anything, even a silly doodle, to represent an unknown.
• So, whatever you do to the right hand side, you have to do the same to the left?
• 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.
• is algebra the same thing as math or a type of math what is the catagory of algebra