Introduction to Equations and Solving Equations

I want to talk about equations. The equation has an equal sign where one side is equal to another side.

A really good way to give an example of equations is with a scale. The scale has one side equal to another.

1. Solve for x:  x - 7 = 12


2. Solve for y:  17 = 12 + y


3. Solve for c:  / 6 - 3c / = / -12 /



Next Lesson: Solving an Equation Using Four Basic Operations
Continue learning.

The transcript of the video.
If they’re not equal the scales are going to show that and they will kind of tilt like that. So here’s an example.

I’ve got this red ball. Plus three little blue blocks on one side. and 5 little blue blocks on the other side. You can see the scale is balanced.

Which means this side’s weight is equal to the weight of that side. That’s why it’s balanced. Now I want to figure out how much is that red ball’s weight.

Well, one thing I could do if I took these blocks away. if I did that to one side then all of a sudden there would be no balance. So that would go up. So if I take 3 blocks away on one side I also need to take 3 blocks away on the other side.

If I’m trying to find exactly what the red ball weighs is I have to get the red ball balance with something on this side That would tell me how much it weighs. Now I’ve got the red ball all by itself.

Well, the red ball is equal to 2 of those blue blocks. That’s exactly what we’re doing with solving equations. We’re basically trying to get the variable alone on one side equal to something on the other side.
And when we achieve that then we basically have found our solution.
Go for example 2Solve
x -2= 6
Solving an equation just means finding the solution. So I’m trying to find a solution that would make this equation true.
What value of x would make this equation true? Now it’s going to be pretty simple.

And the problem is that the beginning will be pretty simple. A lot of them you’ll be able to figure out just on your own using mental math. But that’s not the point.
The point is to learn the process so that when it gets more difficult when you have very difficult equations to solve, you already know what to do.

You know the steps to take to get your solution.

Follow the steps, learn how to solve these equations with easy ones, so that when it gets more difficult, you’ll know what to do. So again the goal. Think of the scale problem.
The goal: I was trying to get the red ball all by itself Everything else on the other side and have it equal. Same thing here.
I need to get the variable alone. That’s the goal one when solving equations.

Right now, x is subtracted by 2.

When you get subtraction I will use the inverse operation.
The opposite of subtraction is an addition.

So if I add 2 to that minus 2 all will go away. Those are subtraction and addition or are inverse operations or opposites in operations. So they would cancel each other out. They would become 0 and we’re are just left with x.

So if I add 2 that goes away and I have X alone but remember on a scale problem when I took two blocks away from one side if I just did that it will become unbalanced. The most important thing with so many equations is that anything I do to one side I do the exact same thing to the other side of the equal sign.

So when I took two blocks away from here I also took two blocks away from here so that it stayed balanced. Same thing here. If I add 2 on one side, I have to add two on another side So those go away. And I have my solution  All I have to do is substitute it. You should never miss an equation. So, it’s my final solution. 

Last Updated on

More GED Prep