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Why aren't we using the multiplication sign?

In algebra, representing multiplication with variables can be tricky due to the similarity between the variable "x" and the multiplication symbol. To avoid confusion, use alternative methods like 2⋅x, 2(x), or 2x. Practice evaluating expressions by substituting given values for variables and following the order of operations. Created by Sal Khan.

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Video transcript

We now hopefully know a little about variables and as we covered in the last video, a variable can be really any symbol, although we typically use letters because we're used to writing and typing letters. But it can be anything from an x, to a y, a z, an a, a b, and oftentimes we start using greek letters like theta. But you can really use any symbol to say Hey, this is going to vary You can take on multiple values But out of all of all of these The one that is most typically used in algebra Or really in all of mathematics is the variable "x" Although all of these are used to some degree But given that x is used so heavily it does introduce a slight problem. And that problem is that it looks a lot like the multiplication symbol Or the one that we use in arithmetic So in arithmetic if I want to write 2 x 3 I literally write "2 x 3" But now that we are starting to use variables, if I want to write "2 times x" Well if I use this as the multiplication symbol it would be 2 times x And the times symbol and the X look awfully similar and if I'm not really careful with my penmanship it can get very confusing. Is this "Two x x"? Is this "two times times something"? What exactly is going on here? And because this is confusing, This, right over here, is extremely confusing And it can be misinterpreted, We tend not to use this multiplication symbol When we are doing algebra Instead of that, to represent multiplication, We have several options. Instead of writing two times x this way, we could write 2 dot x. And this dot, I want to be very clear, This is not a decimal This is just written a little bit higher And we write this so we don't get confusion in between this and one of these variables right here. But this can really be interpreted as "2 times x" So for example, if someone says 2 dot x, when x is equal to 3, well this would be the same thing as two times three, when x is equal to three. Another way you could write it is You could write "2" and then you could write the x in parentheses right next to it. This is also interpreted as 2 times x Once again, so in this situation If "x" were seven, this would be two times seven, or fourteen And the most traditional way of doing it is to just write the x right after the 2. And sometimes this will be read as "2x" But this literally does mean "Two times x" And you might say, how come we didn't always do that? Well it would be literally confusing if we did it over here. Instead of writing "2 times 3" And wrote "2 3" Well, that looks like "23". This doesn't look like two times three And this is why we never did it. But here, since we're using a letter now, It's clear that this isn't a part of that number. This isn't "twenty something" This is two times this variable x. So all of these are really the same expression. Two times x, two times x, and two times x. And so with that out of the way Let's try some few worked examples, a few practice problems And this will hopefully prepare you for the next exercise Where you'll get a lot of chances to practice this. So if I where to say "what is 10 minus three y" And what does this equal when "y" is equal to two Well, every time you see the "y" You'd want that 2 there So this is y is equal to 2. Let's set that y equal to two This is the same thing as 10 minus three times two You do the multiplication first. Multiplication takes precedence in order of operations So three times two is six, Ten minus six is equal to four. Let's do another one. Let's say we had "7x minus 4" And we want to evaluate that when when x is equal to three. Where we see the x, we want to put the 3 there So this is the same thing as "7 times 3" And I'll actually use this notation, so seven times three minus four. And once again, multiplication takes precedence by order of operations, over addition or subtraction So we want to do the multiplying first 7 times 3 is 21 21 minus 4 is equal to 17. So hopefully that gives you a little bit of background, and I really encourage you to try the next exercise, It will give you a lot of practice on being to evaluate expressions like this.