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Lesson 2: One-step equations intuition

# Representing a relationship with an equation

In this lesson, we learn about balancing scales and solving equations. We discover that to find a mystery mass, we can set up an equation using equal signs and balance both sides. By subtracting the same amount from each side, we can solve for the unknown mass, helping us understand the relationship between the two sides of the scale. Created by Sal Khan.

## Want to join the conversation?

• Can we say
X+3=10
• Exactly! Then you need to solve for x. Because one side equals the other, you can do something to the left as long as you do the same thing to the right. If you take 3 away from the left, you also need to take 3 away from the right. Do this and you're left with x = 7.
• 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 !!
• 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)
• 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
• 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.