WEBVTT
1
00:00:00.000 --> 00:00:04.000
Math is cool and you can do it.
2
00:00:04.000 --> 00:00:08.000
All right, this is part two of solving linear equations.
3
00:00:08.000 --> 00:00:13.000
So we're just going to shake it up a little bit over, you know, different possibilities.
4
00:00:13.000 --> 00:00:18.000
Let's see, have this equation. Five equals x minus seven.
5
00:00:18.000 --> 00:00:22.000
Notice the variables on the right-hand side of the equation.
6
00:00:22.000 --> 00:00:27.000
So we still need to isolate it. We just want to know what x equals and I have x minus seven.
7
00:00:27.000 --> 00:00:30.000
All right, so something was subtracted from x to undo it.
8
00:00:30.000 --> 00:00:34.000
We would want to add seven so we would just have x on that side.
9
00:00:34.000 --> 00:00:41.000
But whatever we add to the right-hand side, we have to add to the left-hand side of the equation to keep everything in balance.
10
00:00:41.000 --> 00:00:46.000
So five plus seven is 12 and we have 12 equals x.
11
00:00:46.000 --> 00:00:51.000
But that sounds funny. 12 equals x. I like to write that as x equals 12.
12
00:00:51.000 --> 00:00:57.000
For instance, somebody says, let's say you're 25 years old and someone says how old are you?
13
00:00:57.000 --> 00:01:03.000
You wouldn't say 25 years is my age. You might just say my age is 25 or I'm 25.
14
00:01:03.000 --> 00:01:09.000
So it's better to write it this way. Now, you could even change the problem.
15
00:01:09.000 --> 00:01:17.000
Since these two things are equal five and x minus seven, you could just switch the order and say that's the same thing as saying x minus seven equals five.
16
00:01:17.000 --> 00:01:23.000
If you like to rewrite the problem that way to begin with, that works just as well.
17
00:01:23.000 --> 00:01:31.000
And then you would do the same thing. Add seven to both sides and you have x equals 12.
18
00:01:31.000 --> 00:01:35.000
Okay, so either way. But then we still have to check the answer.
19
00:01:35.000 --> 00:01:41.000
So let's do the check. So now when you do the check, take the original problem.
20
00:01:41.000 --> 00:01:46.000
The original problem was five equals x minus seven. It was not x minus seven equals five.
21
00:01:46.000 --> 00:01:49.000
So you might have made a mistake in your very first step.
22
00:01:49.000 --> 00:01:55.000
You want to, for instance, if you were taking a set of the book, you want to copy exactly what was written out of the book.
23
00:01:55.000 --> 00:01:58.000
Don't look at your own work even.
24
00:01:58.000 --> 00:02:05.000
And underline, make the T. And on the left side, there's nothing to plug in for x. There's just a five.
25
00:02:05.000 --> 00:02:10.000
So you write the five. And on the other side, 12 minus seven. And simplify using order of operation.
26
00:02:10.000 --> 00:02:17.000
Same number on both sides. Means 12 is the answer. So you can write the answer.
27
00:02:17.000 --> 00:02:27.000
The answer is just 12. Or you could put it in braces, which is the more formal way of writing the solution.
28
00:02:27.000 --> 00:02:34.000
Okay, here's one with decimals. Go ahead and put it on pause. Try this on your own and see if you get the right answer.
29
00:02:34.000 --> 00:02:40.000
All right, so what are we going to do here? Well, this time it's nice. We've got the x on the left-hand side.
30
00:02:40.000 --> 00:02:47.000
And we have x plus 4.3. So we need to undo it by subtracting 4.3.
31
00:02:47.000 --> 00:02:52.000
All right, now most people can't do that in their head written in this way.
32
00:02:52.000 --> 00:02:58.000
But notice what I'm doing is I'm adding a positive and a negative number. So we see which one outweighs the other.
33
00:02:58.000 --> 00:03:03.000
And there's more negatives. So we know the answer is going to be negative, right? This side's going to be x equals.
34
00:03:03.000 --> 00:03:12.000
And then what do we do? If you're adding positive and a negative number, you need to subtract.
35
00:03:12.000 --> 00:03:20.000
So we need to do 4.8 minus 1.8. And remember, you line up your decimals. And then we subtract.
36
00:03:20.000 --> 00:03:30.000
So that's going to be 2.5. But since the negative 4.3 was bigger than the positive 4.8, in other words, the absolute value.
37
00:03:30.000 --> 00:03:38.000
It was more negative. The answer is negative 2.5. All right, let's check.
38
00:03:38.000 --> 00:03:47.000
See if that was really the right answer. You copy the original problem and underline it.
39
00:03:47.000 --> 00:03:58.000
All right, so we're going to put a negative 2.5 for x. And now, again, I'm adding a negative and a positive.
40
00:03:58.000 --> 00:04:05.000
So you go over to the right hand side. First of all, it's going to be positive or negative. You have a negative 2.0 something and a plus point 4. There's more positive.
41
00:04:05.000 --> 00:04:13.000
So you know the answer is positive. But when you're adding different signs like this, you have to take their different, subtract.
42
00:04:13.000 --> 00:04:25.000
And so when you subtract that, you do get 1.8. And all right, so on the left side, you get 1.8. On the right side, I get 1.8.
43
00:04:25.000 --> 00:04:36.000
So, yep, I've got the right answer. Negative 2.5 is the answer, not 1.8. So you could write your answer as just negative 2.5 is the answer.
44
00:04:36.000 --> 00:04:50.000
Or you might write that as negative 2.5 using the braces. Not formal, formal. All right, here's one with fractions.
45
00:04:50.000 --> 00:05:00.000
Right, this time, again, the variables on the right hand side. And you have the variable minus 2.5. So we need to undo that minus by adding 2.5 to both sides.
46
00:05:00.000 --> 00:05:07.000
To be different, instead of adding up and down, I'm going to add across this time just because I haven't done any problems in this video like that.
47
00:05:07.000 --> 00:05:17.000
So here was your original problem. To undo what you need to add 2.5 to both sides. All right, so you just have x on this side. So you have to add 2.5 on this side as well.
48
00:05:17.000 --> 00:05:30.000
All right, so on the left hand side, remember how to add fractions? You have to have a common denominator. Hey, cool, we already have that. And then we add the numerators. 2 plus 2 is 4.
49
00:05:30.000 --> 00:05:42.000
So we have x equals 4.5, but remember, we don't want to write it like that. You want to write it as x equals 4.5.
50
00:05:42.000 --> 00:05:49.000
All right, now I want to check and make sure that's the correct answer. So let's do a little check right here.
51
00:05:49.000 --> 00:06:03.000
We have 2.5 equals x minus 2.5. You underline it. Kind of running out of space here, so that's 2.5. And then we plug in 4.5 for x, the answer, right? 4.5.
52
00:06:03.000 --> 00:06:19.000
Minus 2.5. All right, and since it's a common denominator, I get 2.5. Check out. Cool. So the answer is 4.5. So you could either write that as, it's okay with me if you leave it as x equals 4.5.
53
00:06:19.000 --> 00:06:36.000
But some teachers want you to write it more formally or just the number. So I'm showing you. Okay, here's a problem that's a little bit different.
54
00:06:36.000 --> 00:06:48.000
We've got an x-term and a constant on both sides of the equation. So this is a little bit newer. So we want to make sure we have all the x's on one side of the equation
55
00:06:48.000 --> 00:06:59.000
and all the numbers on the other side of the equation. So we've got a 5x over here and a 4x over here. One way of giving them all together is to get rid of it on one side of the equation.
56
00:06:59.000 --> 00:07:11.000
So to not have a 4x on the right-hand side, you could subtract 4x from both sides. So what does that give me now if I just subtract 4x from both sides?
57
00:07:11.000 --> 00:07:25.000
That gives me x minus 2 equals 7. Now this looks like something else we've already done. So now I want to have just to find out what x equals, I'm going to have to add 2 to both sides.
58
00:07:25.000 --> 00:07:40.000
And then we have x plus 0 or x equals 9. Right, maybe that problem a little smaller so we could see the check right to the right of the problem.
59
00:07:40.000 --> 00:07:47.000
So we write the original problem which is 5x minus 2 equals 4x plus 7 and then we're going to replace x with 9.
60
00:07:47.000 --> 00:07:55.000
So on the left side I've got 5 times 9 minus 2 and remember to do order of operations. So we do multiplication first.
61
00:07:55.000 --> 00:08:17.000
45 minus 2 is 43 and over here on the right-hand side we put in 9 for x and that's 36 plus 7 which is also 43. So since I've got the same number on both sides when I replaced x with 9, then 9 is the correct answer.
62
00:08:17.000 --> 00:08:28.000
So we could do just right 9 for my answer or you could use solution sets.
63
00:08:28.000 --> 00:08:36.000
Here's another problem. Again, we've got x is on both sides of the equation but we only have one constant.
64
00:08:36.000 --> 00:08:48.000
So since I've only got variables and that's it on the left-hand side I'm going to put everything on the left-hand side. So that means this 7x plus 7x on this side I'd like to wipe it out from that side.
65
00:08:48.000 --> 00:08:59.000
So if I subtract 7x from both sides, then what happens is I just get again just 1x. Remember 1x is the same as writing x.
66
00:08:59.000 --> 00:09:10.000
If it was a negative one you couldn't just write x. So we have x equals and on this side I've got negative 4 and I'm done. So that was a little bit easier than the previous problem.
67
00:09:10.000 --> 00:09:14.000
Let's check this. I'm going to make this a little smaller.
68
00:09:14.000 --> 00:09:28.000
Okay, so let's put a negative 4 for x. So we have 8 times negative 4 and negative 4 plus 7 times negative 4. Now be careful and do the order of operation very carefully on the right-hand side.
69
00:09:28.000 --> 00:09:35.000
But I'm going to write it as a parenthesis. Maybe that will help. So 8 times negative 4 is negative 32. There's no problem here.
70
00:09:35.000 --> 00:09:44.000
And on the right-hand side remember your order of operations. You need to multiply before adding. So do not add the negative 4 plus 7.
71
00:09:44.000 --> 00:09:56.000
So you've got negative 4 plus 7 times negative 4 is negative 28. And now I'm adding to negative. So it's going to be negative and then 4 plus 28 is 32.
72
00:09:56.000 --> 00:10:06.000
And that's it. Don't assume you did it correctly. And not really do the arithmetic. You really are using the check to help yourself find whether you've got the right answer or not.
73
00:10:06.000 --> 00:10:14.000
That is what is so cool about algebra. When you're solving equations you can find out whether you got it right or not.
74
00:10:14.000 --> 00:10:23.000
And if you got it wrong just start over. Don't even try to find your mistake. That's harder than just wiping out the problem and starting from the beginning.
75
00:10:23.000 --> 00:10:35.000
So the answer to this problem would be just negative 4, right? Or you could write using the braces the formal way of doing it.
76
00:10:35.000 --> 00:10:46.000
Okay, go on to part 3. We're going to be doing a few more problems like this and then going on to a new property of equality.
77
00:10:46.000 --> 00:10:53.000
Called the multiplication property of equality. I hope you learned something. Remember math is cool.