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Studying for a test? Prepare with these 8 lessons on Module 4: Expressions and equations.

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# Combining like terms

Video transcript

Let's say that you
started off with 3 apples. And then I were to give you
another 7, another 7 apples. So my question to you-- and
this might be very obvious-- is how many apples
do you now have? And I'll give you a second
to think about that. Well, this is fairly basic. You had 3 apples. Now, I'm going to
give you 7 more. You now have 3 plus 7. You now have 10 apples. But let's say I want to do
the same type of thinking, but I'm too lazy to
write the word "apples." Let's say instead of
writing the word "apples," I just use the letter a. And let's say this is,
say, a different scenario. You start off with 4 apples. And to that, I add
another 2 apples. How many apples do you now have? Instead of writing apples, I'm
just going to write a's here. So how many of these
a's do you now have? And once again, I'll
give you a few seconds to think about that. This also might be a little
bit of common sense for you. If you had 4 of these apples or
whatever these a's represented, if you had 4 of them and
then you add 2 more of them, you're now going to
have 6 of these apples. But once again, we
started off assuming that a's represent apples. But they could have
represented anything. If you have 4 of whatever
a represents, and then you have another 2 of
whatever a represents, you'll now have 6 of
whatever a represents. Or if you just think of it if
I have 4 a's, and then I add another 2 a's, I'm
going to have 6 a's. You can literally think of 4
a's as a plus a plus a plus a. And if to that, I add another
2 a's-- so plus a plus a, that's 2 a's
right over there-- how many a's do I now have? Well, that's 1, 2, 3, 4, 5, 6. I now have 6 a's. So thinking of it that
way, let's get a little bit more abstract. Let's say that I have 5
x's, whatever x represents. x could be some number. So I have 5 of whatever
that number is. And from that, I subtract 2
of whatever that number is. What would this evaluate to? How many of these
x's would I now have? So it's essentially 5x minus
2x is going to be what times x? Once again, I'll give you a
few seconds to think about it. Well, if I have 5 of something
and I subtract 2 of those away, I'm going to have 3 of
that something left. So this is going
to be equal to 3x. 5x minus 2x is equal to 3x. And if you really think
about what that means, five x's are just x plus
x plus x plus x plus x. And then we're going to
take away two of those x's. So take away one x,
take away two x's. You are going to be
left with three x's.