 # In mathematics, a linear function is a function whose graph is a line. The domain of a linear function is a linear subspace of some vector space, and the range is the set of all points obtained by applying the function to a constant multiple of any of the domain's vectors. The prototypical example of a linear function is the function f(x) = x, which takes the real numbers to the real numbers.

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##### Top Educators  ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University

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we're being asked to solve the given equation. Well, as you can see on the left hand side of the equation, there's a lot going on, so we need to start by simplifying the left hand side. So remember, from the overview, the first thing we want to do is remove our parentheses by using distributive property. Well, it doesn't look like there's a number in front of a parentheses, but just like with variables, when you don't see a number in front, there's really an imaginary one there. So in this case, we really need to distribute the negative one toe both terms in our parentheses. So I'm going to start by bringing down the seven X. Now let's go ahead and distribute well, negative one times. Adx is negative adx and then we have negative one times Negative seven, which is positive. Seven. So again, be careful of your signs. Then we're gonna bring down the minus 13 equals 21. So now we have removed our parentheses. So the next thing I know this is we have, like, terms on the left hand side of our equation. So let's go ahead and combine those well, our first parallel terms are seven x and negative attacks. Well, seven X minus eight X is equal to negative one x so you can even write negative one x or you can simply put negative X. Even one is perfectly fine. For this, uh, example, I'm going to keep it as negative. One x Well, we also have, like, terms for positive seven and negative 13. Well, seven minus 13 is negative. Six. So we'll bring that down as well, Having a little trouble in my marker here. Want to get this working again? So minus six. There we go and it's still equal to 21. And now that we've combined our like terms, as you can see, we now have a two step equation. So the first thing we're going to do to solve is we need to move the negative six to the right hand side of our equation. So they do this. We're going to add six to both sides because negative six plus 60 they cancel out. So I'm gonna bring down the negative one X and then we have 21 plus six, which is equal to 27. So what we're left with is negative. One X is equal to 27 and apologize for this markers. Having a little issue here. There we go. It's like I said, we have negative one X equals 27. So now the last thing you need to dio is to get X all by itself. So they do this. We're going to divide both sides of our equation by negative one, because then the negative ones will cancel out. So on the left hand side, we're just left with X. And on the right hand side, we have 27 divided by negative one, which is negative 27. So now we have solved our equation. So what we found is that our solution is that X is equal to negative 27. So the one thing I want to bring out since my markets being weird again is there are a couple of other options in terms of solving these equations in terms of the steps. But in terms of just having kind of a pattern that you're always going through, it is always nice. Like I said, to remove your parentheses first, Then combine your late terms. So, like I said, we are solution to this equation that we just solved is X is equal to negative 27 Syracuse University
##### Top Algebra Educators  ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University