## Thursday, March 14, 2013

### Algebra Unproject

Hi today I'm going to show you how to solve 3 algebra equations. I'll be teaching you a 2 step multiplying equation, 2 step dividing equation, and a distributive equation.

Definitions
Constant -  A quantity that does not change its value.
Coefficient -  A number multiplied by a variable in an algebraic expression.
Variable - A letter or symbol used to represent a number.
Distributive Property - The sum of two addends multiplied by a number is the sum of the product of each addend and the number.
2 step multiplying equations
6r + 6 = 18
First you isolate the variable, by isolating it you make a zero pair for your constant, then you do it on the other side because you did it there.
6r + 6 - 6 = 18 - 6
6r = 12
Then you balance it by dividing both sides by the coefficient then you fully have your variable isolated
6r = 12
6       6
r = 2
Now we verify it, first you rewrite your equation
6r + 6 = 18
Now substitute your variable with 3
6(2) + 6 = 18
Now you multiply your coefficient by 2
12 + 6 = 18
18 = 18
2 step dividing equations
m + 2 = 18
3
First you want to isolate the variable by making a zero pair for your constant then you do the same thing on the other side
m + 2 - 2 = 18 - 2
3
m = 16
3
Then you it by multiplying your variable and you do the same thing on the other side
(3)m = 16(3)
3
m = 48
Now you verify it, first you rewrite your equation
m + 2 = 18
3
Now substitute your variable with 48
48 + 2 = 18
3
16 + 2 = 18
Then you verify it by adding the coefficient with the constant
18 = 18
Distributive Property
Now I will teach you about distributive equations
4 (m - 3) = 12
First you multiply the constant and the variable by the coefficient.
4 (m - 3) = 12
m - 3
m - 3
m - 3
m - 3
You would get
4m - 12 = 12
Then solve it like a 2 step multiply equation
4m - 12 + 12 = 12 + 12
4m = 24
4m = 24
4         4
m = 6
4m - 12 = 12
4(6) - 12 = 12
24 - 12 = 12
12 = 12
Now I will do in a diagram

4 (m - 3) = 12
Now you do the same steps as you would do on the 2 step multiply equation.
4 (6 - 3) = 12
4 (3) = 12
12 = 12