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We now hopefully know a little about variables

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and as we covered in the last video, a variable can be

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really any symbol, although we typically use letters

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because we're used to writing and typing letters.

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But it can be anything from an x, to a y, a z, an a, a b,

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and oftentimes we start using greek letters like theta.

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But you can really use any symbol to say

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Hey, this is going to vary

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You can take on multiple values

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But out of all of all of these

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The one that is most typically used in algebra

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Or really in all of mathematics

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is the variable "x"

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Although all of these are used to some degree

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But given that x is used so heavily

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it does introduce a slight problem.

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And that problem is that it looks a lot like the multiplication symbol

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Or the one that we use in arithmetic

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So in arithmetic

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if I want to write 2 x 3

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I literally write "2 x 3"

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But now that we are starting to use variables,

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if I want to write "2 times x"

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Well if I use this as the multiplication symbol

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it would be 2 times x

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And the times symbol and the X

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look awfully similar

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and if I'm not really careful with my penmanship

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it can get very confusing.

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Is this "Two x x"?

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Is this "two times times something"?

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What exactly is going on here?

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And because this is confusing,

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This, right over here, is extremely confusing

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And it can be misinterpreted,

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We tend not to use this multiplication symbol

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When we are doing algebra

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Instead of that, to represent multiplication,

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We have several options.

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Instead of writing two times x this way,

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we could write 2 dot x.

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And this dot, I want to be very clear,

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This is not a decimal

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This is just written a little bit higher

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And we write this so we don't get confusion

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in between this and one of these variables right here.

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But this can really be interpreted as "2 times x"

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So for example, if someone says

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2 dot x, when x is equal to 3,

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well this would be the same thing

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as two times three, when x is equal to three.

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Another way you could write it is

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You could write "2" and then you could write the x in parentheses

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right next to it.

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This is also interpreted as 2 times x

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Once again, so in this situation

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If "x" were seven, this would be

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two times seven, or fourteen

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And the most traditional way of doing it

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is to just write the x right after the 2.

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And sometimes this will be read as "2x"

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But this literally does mean "Two times x"

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And so wait a minute, how come we didn't always do that?

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Well it would be literally confusing if we did it over here.

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Instead of writing "2 times 3"

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And wrote "2 3"

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Well, that looks like "23".

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This doesn't look like two times three

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And this is why we never did it.

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But here, since we're using a letter now,

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It's clear that this isn't a part of that number.

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This isn't "twenty something"

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This is two times this variable x.

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So all of these are really the same expression.

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Two times x, two times x, and two times x.

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And so with that out of the way

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Let's try some few worked examples, a few practice problems

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And this will hopefully prepare you for the

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next exercise

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Where you'll get a lot of chances to practice this.

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So if I where to say "what is 10 minus three y"

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And what does this equal when "y" is equal to two

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Well, every time you see the "y"

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You'd want that 2 there

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So this is y is equal to 2.

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Let's set that y equal to two

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This is the same thing as 10 minus three times two

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You do the multiplication first.

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Multiplication takes precedence in order of operations

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So three times two is six,

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Ten minus six is equal to four.

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Let's do another one.

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Let's say we had "7x minus 4"

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And we want to evaluate that when

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when x is equal to three.

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Where we see the x, we want to put the 3 there

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So this is the same thing as "7 times 3"

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And I'll actually use this notation, so seven times three minus four.

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And once again, multiplication takes precedence

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by order of operations, over addition or subtracition

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So we want to do the multiplying first

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7 times 3 is 21

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21 minus 4 is equal to 17.

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So hopefully that gives you a little bit of background,

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and I really encourage you to try the next exercise,

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It will give you a lot of practice

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on being to evaluate expressions like this.