What are variables, expressions, and equations? | Introduction to algebra | Algebra I | Khan Academy

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put a 1 in its place. -2 2. Which is 3. and the equation. and it is then negative 2. and z = 2 can be. do more complex things. minus x like it. of this variable. of x. variable When we work with basic accounting we see the concrete numbers. We see 23 + 5 and know that the numbers are just here and we can then calculate the numbers. The answer is 28. We can say 2 x 7. We can say 3/4. In all these cases we know exactly with what numbers we are working. As we enter the Algebraic world, and you have probably seen a small part of it, we start working with the idea of \u200b\u200bvariables. When we say “variables”, and there are quite a few ways what we can think about them, then we actually talk just about different values \u200b\u200band expressions about how these values \u200b\u200bcan change. The values \u200b\u200bin these expressions may change. For example, when I write x + 5 then it is an expression. This expression can have a certain value that depends of the value of x. For example, if x is equal to 1, then x +5, our expression here, be equal to 1. The reason is that x’s value is now 1. It will be 1 + 5. So x + 5 will be equal to 6. If x is equal to, for example -7 then x plus 5 will be equal to, well x is now -7. It will then be -7 +5 Take note. x is the variable in this case, and the value can change as the context changes. And this is in the context of an expression. You will notice that in the context of an equation, is it very important to realize that there is a difference between the expression An expression is really just an assertion about values, an assertion about a certain type of quantity. So that’s an expression. An expression would be something like well, what we saw here. x + 5 the value of this expression will change depending on the value And you can only evaluate it for different values Another expression could be something like maybe I do not know y + z. Now everything is variable. If y is 1 and z is 2, then it will be 1 + 2. If y is 0 and z is -1 then it will be 0 + (- 1). These can all be evaluated and it will basically gives you a value that depends on the values \u200b\u200bthat each of these variables has what this expression consists of. In a comparison, you are basically equate expressions with each other. This is why they are called “equations”. You make two things equal. In a comparison you will see that one expression is equal to another expression. For example, you could say something like. . . x + 3 = 1 and in this situation where you make a comparison where you have a comparison with only one however, you can work out what x should be in this case. and you can even do it in your head. What do you have to add to 3 to get 1? well you can do that in your head. if I have that -2 + 3 equals 1 so in this context a comparison is underway to limit the value of this variable but it does not necessarily have to be so restrictive. You can have something like, x + y + z = 5 now you have this equation that is equal to the other expression. 5 is actually just an expression on the right. and there are some limitations. If someone tells you what y and z are and you go x gets value. If someone tells you what x and y are is going to limit what z is. However, it depends on what the different things are. As for example if we say y = 3 what will x then be in this case? so if y = 3 then you will have that the left side of the expression x + 3 + 2 is and will be x + 5 this section here is going to be 5 x + 5 = 5 and so what + 5 = 5? well now we’re limiting it x will have to … x will have to be equal to 0 But the important point here, one what you will hopefully realize is the difference between an expression and an equation An equation is basically that you equate two expressions. the important thing to remember here is that the variable can have different values depending on the context of the problem. and to just confirm the point again, let’s just evaluate some expressions, when the variables have different values. For example, if we use the expression if we use the expression, x to the. . . x to the power y has if x is equal to … if x is equal to 5 and y is equal to 2 y is equal to 2. then our expression will have value here Well x is now going to be 5 x is now going to be 5. y will be 2 and it’s going to be 5 to the second power whether it will simplify to 25. if the values \u200b\u200bchange, if we say, x … if we say, let me do it in the same color. If we say x is equal to … x is equal to and y … and y is equal to 3 then this expression will simplify to, then it will simplify after, let me do it in that (color) so it will simplify to -2 this is what we are now going to replace the x with in this context. and y is now 3 -2 to the third power … -2 to the third power it is -2 x -2 x -2 which then is -8 -2 x -2 = +4 x -2 is again equal to -8 is equal to -8 so you see that depending on what the values of this is, we can even we can have expressions like, the square root of x + y and then if x is equal to, let’s say x is equal to 1 and y … y is equal to 8 then this expression will simplify to well every time we see an nx we want to so we will have a 1 here. and you will have a 1 here. and every time you see ‘ny. you will put an 8 in its place. and in this context, we place these variables so you see an 8. so under the root you will 1 + 8, so you will have the positive root of 9. so this whole thing will simplify you in this context we replace these variables with these numbers simplifies this whole thing to be 3 1 plus 8 is 9 the positive root of it is 3 and then you will have that 3 – 1 what is equal to … what is equal to

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