814 Math Blog (2012): March 2013

Monday, March 18, 2013

If you need more explanations on how to do 2-step equations, it's as easy as:
Isolating the variable(Charlie)
Cancelling the constant (Patrick)
Balancing and simplifying
Cancelling the coefficient(Sam)
Balancing and simplifying again
then checking your work

Ryan's Unproject Algebra

The adventures of Algebra. (With characters of Dora)

       "Hey Boots do you know how to do one of these things: Two step equation, Distributive and modeling?" said Dora

      "Yes I do Dora. Ill teach you how to do Two step. Lets try this question 4x -2 = 18" said Boots.

      "First we do is isolate the variable. The variable is (X). Second is cancel the constant which is -2 with a zero pair which is +2 and add 2 to the answer which becomes +20." said Boots.

       "Than we cancel the Coefficant which is multiply by 4 but we cancel it with divide by 4. 4x = 20 becomes 4x/4 = 20/4. You balance the equation again. (Reason why I use a backslash instead of the line because I was a bit to bored. They are whole fractions which makes x=5. We would simplify if the answer is a decimal." said Boots.

       "It is time to verifty. We would rewrite the question 4x-2=18. Then we substiude x which be 5 and it would be 4(5)-2=18. Than we multiply 4 and 5 together we will get 20. Than all we have to do is to minus 2 from 20 to get 18. 20-2=18. Now we will get the answer which is 18. 18=18" said Boots.

"Thanks Boots I know how to do 2 step now. Now teach me how to do distributive" said Dora. I'll show you how to do distrivutive. Lets do this questions 5(x+6)=20." said Boots

"First we will do five times x and five times 6. We will get 5x+30=20. Now cancel the constant 5x+30-30=20-30 you will get -10. You can now divide the coefficant 5x/5 = -10/5. X is -2. We would rewrite the original question 5x+30=20. Substiude the x with -2. It would be 5(-2)+30=20. We multiply 5 and -2 and we would get -10.It would be now -10+30=20. Since it is a negative you minus 10 from 30 and you will get 20 and the answer is 20" said Boots.

"Wow your really smart Boots. said Dora. Haha thanks Dora this is going to be the last thing I help you is my pesonal hardest. It is modeling. It's where you dra. Lets do 3x-3=9" said Boots.

We would draw the question out.

Now we cancel the constant with a zero pair.

Than we share our circles into even groups of 3 Than circle one group.

Than we will get what is X.

"Thanks Boots your really smart and this will help me do my test" said Dora.

Sunday, March 17, 2013

I will show you how to solve and verify a two-step equation, show how to model, show Distributive Property.

First let's try a Two-Step Equation.

Ex. 2x + 4 = 4

But first, let's write some facts about those numbers first.

This Number 2 in 2x is called a Coefficient. The Coefficient is by the letter, which is called a Variable. The Variable represents an unknown number. We won't know the number until after we solve the equation. The Coefficient is a letter that is used to multiply a variable. You can cancel it by using the opposite integer. The Constant is the factor of the Equation that never changes.

2x + 4-4 = 4-4 = 2x = 0 so x = 0.

Now we verify.
2x + 4 = 4
2(0) + 4 = 4
0 + 4 = 4
4 = 4

Now I will show how to divide with fractions in algebra.

Let's list some points down first.

Isolate
Cancel the constant with a zero pair
Balance
Cancel, divide with multiply
Balance again
Simplify
Verify

Ex. x/4 + 5 = 10
x/4 + 5 - 5 = 10 - 5
5x = 5
4
x = 20
x/4 + 5 = 10
20/4 + 5 = 10
5 + 5 = 10
10 = 10

Now let's try Distributive Property.

2 (x + 3) = 10

2 groups of x + 3 = 10
x + 3
x + 3
2x + 6 = 10

Now you solve it using two step equation.

2x + 6 - 6 = 10 - 6 = 2x = 4 Divided by 2
x = 2
Now Verify.
2x + 6 = 10
2(2) + 6 = 10
4 + 6 = 10
10 = 10

Thursday, March 14, 2013

Two Step Algebra Can

Two Step Algebra

Question 1:

4x - 4 = 0

4x - 4 + 4 = 0 + 4

4x = 4

4 4

x = 1

Verify:

4x - 4 = 0

4(1) - 4 = 0

4 - 4 = 0

0 = 0

Question 2:

10x - 15 = 35

10x - 15 + 15 = 35 + 15

10x = 50

10 10

x = 5

Verify:

10x - 15 = 35

10(5) - 15 = 35

50 - 15 = 35

35 = 35

Question 3:

r - 6 = 7

-3

r -6 + 6 = 7 + 6

-3

r = 13

-3

(-3) r = 13 (-3)

-3

r = - 39

Verify:

r - 6 = 7

-3

39 - 6 = 7

-3

-13 - 6 = 7

7 = 7

Dawsons Algebra post

i zero paired the constant by adding +5 and balancing it by adding +5 to the answer, then i simplified it. i then canceled the coefficent by dividing it, and doing the same to the answer.

that's how i isolated the variable. then i finished it off by verifying to see if my calculations were correct.

in intergers, how come two negatives equal a positive, and would two positives equal a negative or?