00:01
Here we have a few equations and we want to see if x is all real numbers, x is 4, or if there is no solution.
00:08
So the first one we have is written here.
00:10
Let's simplify this out.
00:12
So what we're going to do first is foil this.
00:16
So we're going to get 2 times 3x is 6x and then 2 times negative 2 is negative 4.
00:23
Now we're going to subtract 6x on both sides.
00:27
We actually see that they both cancel out so we get negative 4 equals negative 4.
00:33
Now this is just a true statement.
00:35
We do not have an x in here.
00:37
We do not have x equals 4.
00:39
Nothing like that.
00:40
We just have negative 4 equals negative 4.
00:42
That is always true.
00:44
So that means no matter what x is this statement is going to be true.
00:48
So x is going to be all real numbers.
00:49
That was the first one.
00:51
Now let's do the second one.
00:53
Okay, again, let's foil these out.
00:56
3 times 5x is going to give you 15x plus 3 times 2 is going to give you 6 equals same thing, 15x, except over here we're going to get negative 20, 5 times negative 4.
01:12
So let's get the x's on one side, minus 15x minus 15x, and already we could see an issue here.
01:21
We are left with 6 equals negative 20 because this cancels out and this cancels out.
01:31
So this is a false statement.
01:33
6 never equals negative 20.
01:35
And what this means is no matter what x is, we're going to get 6 equals negative 20, which is not true.
01:41
Therefore, x has no solution.
01:45
There's no x you could plug in here to make this a true statement.
01:48
So now let's do the next one.
01:50
Okay, x minus 2x equals 2x minus 8.
01:54
Already we could see that this isn't looking too good because this is the negative version of this, but let's try to solve it out.
02:03
So we can add 2x to both sides.
02:08
All right, so we know that this is not going to be all x's, so let's see which of the other ones it is...