5

2.y = 3(x+2) + 1...

Question

2.y = 3(x+2) + 1

2.y = 3(x+2) + 1



Answers

$$ (y+2)(2 y+1) $$

Given y equals three x plus four. We're going to use a graphing calculator to graph the equation and take a look at what we see. Are you going to use Desmond's dot com here too graphic? It's easy to use very user friendly and we're just in this box going to type Y equals three X plus four and it graphs it for us. And then we can take our mouse. We can either use these pluses and minuses or you can use the scroll feature on your mouth and we can zoom out to look at it. Or we can zoom in. So if we zoom out, we can see that it just is a straight line with a slope that goes on forever in both directions. And if we zoom in, we can take a look at the intercepts and we see that we have that intercepted 04 right there. That's our why intercept. And then we have this intercept at negative 1.33, so negative 4/3 comma zero. And this is what the graph of Y equals three, X plus four. Looks it has a slow book three And AY intercept of four.

That this problem We want to solve an equation by by combining like terms, let's take the equation. Two plus three equals two y plus one minus y. In this problem, we can combine the two and three on the left side, which makes five. And we can also combine the two y and the minus y on the right side. Which two. Y minus one y is a one y or why bring the plus one down now? Let's in fact, one off both sides to get the Y by itself. And five minus one is four, so Y equals four.

We're being asked assault to given equation for why? So they do this. I'm first going to subtract three from both sides of our equation. So we're gonna be left with 1/2 y is equal to while four minus three is just one. Now, to get rid of this fraction, I'm gonna multiply both sides by two. Because take a look at what happens while two times 1/2 is just one. So these cancel out and we're just left with why? And then on the right hand side, we have one times two, which is two and now have solved our equation for why, and we found our solution to this equation is too.

So before I clear denominators. Eventually in a factor. The denominators. So I know what I need to multiply by. Why squared minus y minus two and looking for factors of negative to that have to negative one. So that would be negative too. And positive one. So why minus 2/10? Y plus one is the factory ization of y squared minus y minus two. All right. Next up. Why squared? Minus four? That can be written as. Why minus about why? Plus two times y minus two. And nothing. The factor over here on the right. OK, so let's give myself some room. Actually, move that over here a little bit. All right? So I need to multiply everything by. Why, minus two. That will cancel that. Those will cancel. All right, Next up, let's multiply everything by y plus one. Those will cancel as well. These. And then we still got to get rid of that wide. Plus to their soul. Multiple everything by why? Plus two. I was Well, cancel. Can I had a room here, and I Okay, this isn't so bad. It looks really bad, but we've got why, plus two times y plus two. Okay, Squaring binomial. Perfect square. Try no meal pattern here. Why squared? Plus four X plus four. What I have here. Y plus one times Y plus one is all this left. Okay, Wife plus one squared is why squared. Plus two X plus one. And on the right, we have Y plus two times Y minus two. We already know that. That's why squared minus four. All right, well, we can fix some things real quick. Here. Got why squares on both sides of this equation. We got, um That's it, actually. So let's combine like terms on the left. I got the y squared. I've got four x and two X, which makes six sex, and I've got four and one, which makes five. And let's also add affordable sides. Why squared? Plus six X plus nine equals zero. Uh, that's a perfect square Try. No, no, It could be written as why plus three squared equals zero. So we can solve this equation using zero product property. We know that Why would have to be negative three on. That's our solution. Negative three


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