00:01
All right.
00:02
In this question, we are being asked to solve the equation of 6 equal to a negative 4 times 1 minus x.
00:16
And then we're going to add to that a 3 times the quantity x plus 1.
00:22
And our first step in solving any equation is to simplify both sides of the equal sign.
00:30
So the left -hand side only has a six on it.
00:33
That is as simplified as it can get.
00:35
The right -hand side has two separate parentheses.
00:39
So we need to take care of those.
00:41
And then we need to, once we've distributed, we need to look to see if there are any like terms that need to be combined.
00:48
So the first step in simplifying the right -hand side, as i said, is going to be to use the distributed property.
00:55
So i'm going to take this negative 4, and i'm going to distribute it into the parentheses.
01:01
So i'm going to multiply everything in the parentheses by negative 4.
01:05
And i'm going to go ahead and rewrite my equation as i do this.
01:09
So 6 equals, and then i have a negative 4 times 1, which is negative 4, and a negative 4 times a negative x.
01:21
A negative times a negative is a positive, and that's going to be a 4x, plus, and then we get a repeat the same thing, this time multiplying a 3 into its parentheses.
01:35
So 3 times x is 3x and 3 times a positive 1 is a positive 3.
01:46
All right.
01:47
So now that i've distributed and i've gotten rid of the parentheses, i need to look and see on the right hand side if there are any like terms to be combined.
01:57
So the first thing i want to do is i want to kind of identify what my like terms are.
02:01
So i have a negative 4.
02:03
So i have a number, i have a constant.
02:06
Are there any other constants or numbers without variables? well, my second term is a 4x, so it's got an x, then i have a 3x, and then i have a 3.
02:16
So i'm going to go ahead and circle the 3 because it's like to the negative 4.
02:21
And i'm going to go ahead and underline my 4x and 3x because those are like terms to each other as well.
02:28
So i've identified what my like terms are now i need to combine them.
02:33
So again, i'm going to just bring down my six equal to, and i can't forget about that.
02:39
And then i have a negative four plus a three.
02:44
So negative four plus three is negative one.
02:48
And i'm going to go ahead and cross those out because i like to just like i've used them.
02:52
I'm done with them.
02:53
I don't want it there confusing my brain.
02:56
All right.
02:57
And then then my second set of like terms are the xes.
03:04
So i have a 4x plus a 3x, positive 4x plus a 3x is a positive 7x.
03:14
All right.
03:16
So i have now simplified that right hand side.
03:20
I'm left with a negative 1 plus a 7x.
03:23
Those are not like terms, so it's as simplified as it can get.
03:27
And i can switch gears a little bit and go into the solving, which is what the question asked us to do in the first place...