Presentation about equations:

I'm going to tell you something more about equations. About what it actually is, how it works and other things.
I'm also going to tell you something about how equations actually are related with ratios.

What is an equation?

An equation represents two expressions but they are separate with the sign =.
Equations also can be represented as linear graphs.
It represents to see the relationship between variables (like x,a,z etc.) and numbers ( 2.9.5).
It is when you have a visual representation of a formula showing an alike problem on both sides.
The expression on the left side of the = has the same value then on the right side of the =.

With an equation it can happen that your answer is x=o
And if the final answer is 3x=7 then it's actually going to be x= 7/3

For example: x=9 or x=4
You also have some complicated equations like 2(2x+7)=$=3x which is connected with the Distributive Property but you will learn that later.
external image images?q=tbn:ANd9GcQgzac_tOzEdwcXvFwg99Cc46SImOCR8zQUe5J6IaKbA1czNxULqg

How to make/find the equation:

For example if you have 2x-3=6x+4
  • The first thing that you want to do is: All the x-es or all the z-es or.. put together on one side. Most of the times it's the variables on the left and the numbers on the right.
  • If you have done that then you also need to make it positive if its negative and make it negative if it's positive, that means that if you want to put 6x to the other side then its going to change to -6x.
  • So if you look at the example then that is going to be: 2x-6x-3=4 -->that's what you get if you put all the variables on one side.
  • But you need to do the same with the numbers, if you have -3 and you need to do that to right side then its going to be +3
  • if it's on the operation + then it's going to be - on the opposite side.
  • This is the result when you have done that: 2x-6x=4+3
  • You can replace the numbers and the variables on the same time, that's not going to change anything.
  • When that is done it's much easier. You just need to do the variables together and numbers together.
  • So this is what your result must be: 2x-6x= -4x and 4+3=7
  • So: -4x=7 (sometimes you can simplify it but now you can't do that)

external image images?q=tbn:ANd9GcTw2_-m3yp5ohOrru7YVXxUTEH9jKRgBzwLkWmay7y1esWCuiCFXw

Here is another example of how to do it:

First of all: 6x+8x=12+4
That's going to be: 12x=16
But you can simplify that: You can do 12 divided by 4 and you also can divide 16 by 4.Result is 3x=4
After that you can't going farther.

How are equations actually related with proportions:

What an proportion actually is, it is an equation with a ratio on each side of the =.
It's a statement that 2 ratios are equal or the same. And with an equation that's actually the same. The variables on the left side is normally the same on the right side.

Some really important things to remember if you want to solve equations:

  • if you need to do for example 6*x then it's going to be 6x
  • With solving equations, people learned to subtract and add to both sides ( you can only do it to one side because if you do it on the side where the number is from then it's always going to be 0 so that doesn't really matter.
  • Here is an example that you can understand it more. If you have 4x-6=8, then you can do: 4x+6=8+6 You don't need to do it.

You have all different sort of equations:

It all can get more difficult.
  • The easiest one is just 6x+4 and you can't change anything on that.
  • The beginning is 6x+4= 8
  • A bit more difficult is 6x=4=8-3x+4
  • More complicated: Equations with brackets. If you have equations with brackets like 4(2x+5)=6x - 4 then you just first need to do the brackets.
  • You actually want to do the brackets away and you can do that with multiplieng the number right before the brackets times the first number in the brackets so here that would be 4*2x and that is 8x but you also have the other number so you need to do 4*5=20. What you would have on the left side of the = is then 8x+20.
  • Another really important thing if you have brackets in your equation is that you can have a number before you brackets. Then you just need to do the number times the numbers in the brackets but it also can happen that you have for example: 5-(2x+5)=.. you see that you now have a minus before the brackets, that means that you need to do the minus*the operations before the number or variables in the brackets. So here you do the minus*the operation by 2x and that is positive so you need to do + * - = - (+*+=+ and -*-=- and +*-=-)
  • You have that also with +, but that is easy. If you have a + before the brackets then you just write the equation without brackets. It all stays the same, so for example: 8x +(3x+9)=8-2x, that would just be 8x+3x+9=8-2x
  • What you need to remember is: 9x*7t= 63xt

Another sort of equations is the linear equation:

I just will explain it really short, and there is the really good video which explains it very well so look at the video for sure.
A linear equation has 2 or more variables, a slope and an y-intercept. For a linear equation you most of the times use mx+b. M=is your slope, x is just your number and b is your y intercept.

external image images?q=tbn:ANd9GcS9PWZconDCDBmqbu0UYIIsbZ5xDVClW6XgMXr8OzVFQeNNnrUMcA

Some more information about equations: video.
You can learn it on other ways then the way on this wiki. On this video it's a bit different.

Here, if you wanted to understand it more and practice more, here are some equations with and without brackets.
external image equations-with-brackets.jpg