Please solve and explain how they were done.
4x - 8 = - 32 + 2x
- 3(1x + 3) = - 33
3x + y = 5
- 3x - 2y = -1
1. 4x - 8 = - 32 + 2x
Ok, first of all we need to collect "like-terms", that is, move all the x's to one side and the numbers to the other.
So we get: 4x - 2x = -32 + 8
This means that 2x = -24, then divide both sides by 2, we get:
x = -12
2. - 3(1x + 3) = - 33
Divide both sides by -3, we get (1x + 3) = 11
1x = 11 - 3, which is the same as x = 8
3. Solve: 3x + y = 5 and -3x - 2y = -1
Ok, these are what we call simultaneous equations and the method I'll be using is one of the methods know as substitution, first of all, from 3x + y = 5, we can see that y = 5 - 3x, this means whenever we see y in the second equation we can replace with 5 - 3x, so -3x - 2(5 - 3x) = -1.
Expandinf your brackets, -3x - 10 + 6x = -1, and then collect like terms as before: 3x = 9, giving x = 3
1. 4x - 8 = - 32 + 2x
Ok, first of all we need to collect "like-terms", that is, move all the x's to one side and the numbers to the other.
So we get: 4x - 2x = -32 + 8
This means that 2x = -24, then divide both sides by 2, we get:
x = -12
Q: 32 - 8 = 24 and 24 : 2 = 12 got it
2. - 3(1x + 3) = - 33
Divide both sides by -3, we get (1x + 3) = 11
1x = 11 - 3, which is the same as x = 8
Q: Not that I doubt it but in what way does (1x + 3) = 11?
3. Solve: 3x + y = 5 and -3x - 2y = -1
Ok, these are what we call simultaneous equations and the method I'll be using is one of the methods know as substitution, first of all, from 3x + y = 5, we can see that y = 5 - 3x, this means whenever we see y in the second equation we can replace with 5 - 3x, so -3x - 2(5 - 3x) = -1.
Q: 3x + y = 5 and -3x - 2 ( 5 - 3x) = -1 got it.
( 5 - 3x) becomes 10? and where is 6 coming from?
Expanding your brackets, -3x - 10 + 6x = -1, and then collect like terms as before: 3x = 9, giving x = 3
I get -3 -10 +6 = -3 but not so much 3x = 9
First of all, I've assumed you can do basic algebra seeing you're asking questions that require them. But I'll explain in a little bit more detail:
First Question: 4x - 2x = -32 + 8, the left hand side says "4 lots of x's take away 2 lots of x's" which gives "2 lots of x's" and the right hand side is a simple addition, -32 + 8 is -24.
So we get: 2x = -24 (the minus sign in front of the 24 is crucial), and now if we divide both sides of the equation by 2, we get x = -12
This is once again a simple division on both sides of the equation, you're given the - 3(1x + 3) = - 33, Dividing the left hand side by -3, we get 1x + 3 on the left, and dividing the right by -3, we get 11...
Ok, first of all, where did the 10 and the 6 come from? The answer is simple: the equation I want to solve is this: -3x - 2 ( 5 - 3x) = -1, notice there is a 2 outside the bracket: 2 ( 5 - 3x), so what that means is, we need to "expand our brackets", once again, basic algebra.
In words, that's saying 2 lots of 5 - 3x, but 2 lots of 5 - 3x is the same as saying 2 lots of 5's minus 2 lots of 3x's, mathematically: 2(5 - 3x) = 2*5 - 2*3x = 10 - 6x
Your second question: -3 -10 +6 = -3, I'm assuming this is in relation to -3x - 10 + 6x = -1, this equations has x's in them and non x's in them, the -3x and the +6x, as well as the -10. When you look at something like that, you simply cannot ignore the x's.
So first thing is to put all the x's to one side and all the numbers to the other side. -3x - 10 + 6x = -1 becomes: -3x + 6x = -1 + 10
The reason why we can't add x's and numbers together: think of x's as apples and numbers as oranges, they're 2 different things, if someone asked you how many apples is 3 apples + 2 oranges... you can't answer 5 apples, because oranges aren't apples.
So this is why we get -3x + 6x = -1 + 10 and not just -3 + 6 = -1 + 10.
Solving -3x + 6x = -1 + 10, you get on the left hand side, 3x, and on the right hand side, 9. so -3x + 6x = -1 + 10 is the same as saying 3x = 9.
Thanks. That helps a lot. I'm familiar with some of it but I'm still pretty new at this.
I've got a lot of spare time and I'm not taking any Algebra class or doing this because I have to. I'm always getting curious about strange stuff, like chinese characters, musical writing and even Algebra and whatever. I figured it couldn't hurt to learn a little bit about it so I just wanted to know what the big deal is. So I went and bought a couple of books "Algebra and Calculis for Dummies " and even went to Online Algebra Worksheet Generator and made one of each type of problem here. So far it seems pretty interesting.