Modeling two step equations

0:00- [Narrator] What we're gonna do in this video is solve the equation. Negative six is equal to four and plus six, but we're gonna do it in a visual way to think about how we're solving this algebra. So what I could do is I'm going to set up an equality and just represent the same thing, but do it visually.

0:18So the negative six part, I could represent that as six squares here. Each of these six squares represents negative one. Let me write that real fast. Each of these are negative one, and then four Ns. Well, I can make a block like this to represent an N. So one, two, three and then four.

0:45Each of these are Ns. And then last but not least, I have this positive six here. So once again, I'll do six blocks, but each of these represent a positive one, not a negative one. So each of these are a one. Now, the first thing that I wanna to do, well if I wanna solve this for N, I first want to get all of the Ns on one side and all of the constants on the other.

1:11So ideally I want to get rid of these six one blocks or get rid of this positive six. Well, one way is to just subtract six from that right hand side. But if I wanna maintain this equality, anything I do to the right hand side, I have to do to the left hand side.

1:25So if I were to write it out algebraically, I could say, hey, I am going to add negative six to both sides, or another way to, I could subtract six from both sides. Well, if I were to do that, if I were to add negative six to both sides on this side, I'm going to have six more of these negative blocks, negative one blocks.

1:47So let me draw it like that. Negative one, negative one, negative one, negative one, negative one and negative one. But I'm also gonna have six of them over here, two, three, four, five and six. Negative one, negative one, negative one, negative one, negative one, and negative one.

2:08Now what's interesting about that is these blue box and the salmon color blocks, these are going to cancel out, each of these one and a negative one. That's zero, one and a negative one, that's zero. That's why we added the negative six to both sides, or why we subtracted six from both sides.

2:27So on the right hand side, we are just going to be left with the 4N. And maybe I'll do that in that same color that I'm representing it in, 4N. And then that's going to be equal to, what do we have on the left hand side? Well, now we have 12 of these negative one blocks, so this is going to be equal to negative 12.

2:48Now the next thing we might wanna say is, hey, how do we solve for N? We get 4N is equal to negative 12. That's what's left over here. Well, what if we divided both by four? If we divide both sides by four, that would be analogous to let's split each of these sides into four equal groups.

3:09So like that, like that, like that on that side. And then like this, that, and that on this other side. Remember, all of these blocks have disappeared. And when you do that, you see that each of these Ns, when you take the two things that are equal to and you divide by four, each of the Ns is equal to three of these negative one blocks.

3:34And so we get N is equal to negative three, which is exactly what you would've gotten if you divided both sides of this equation by four. And we're done, we've solved for N.