### Rainer's Growing Post ( 3 )

Both of algebraic equation and expression has all variable, constant ( starting point ), and coefficient ( change ). What varies is the variable. The letter of the variable doesn't matter. What matter is that does the variable in an algebraic equation or expression given. In an expression the variable could be something you choose. In an equation the value of the variable is already given to balance each side of the equal sign.

example :

5x + 5 = money

The expression above has coefficient ( first 5 ), variable ( x ), and constant ( last 5 ). In this expression the variable represent the amount of months.

5x + 5 = money

5(1) + 5 = money

5 + 5 = money

10 = money

Now here an example of an equation. Remember that the variable has already a value.

5n = 5

5n/5 = 5/5

1n = 1

n = 1

2. What is a variable and why do we use one in algebra?

Variables are any letter ( a - z ) that represent numbers. They differ so you can represent it with any number instead. In an algebraic equation you are solving what the variable represent. It already had a value in an equation. In an expression you choose what the variable represent like the example in question 1.

3. Solve for N

Circle ( c ) = 1

Square ( s ) = 2c = 2

In the first diagram, the right side has 9 c or 9. The left side has 2 s and a triangle ( t ). 2s is equal to 4.

9 - 4 = 5

Triangle ( t ) = 5

In the second diagram, the right side has 6s or 12 and 2t or 10.

12 + 10 = 22

There are 2n in the other side. So 2n = 22.

2n/2 = 22/2

1n = 11

n = 11

4. Solve the following equations. Show all of the steps that are needed.

a.) 3n + 4n + 7 = 2n + 12

3n + 4n + 7 = 2n + 12

7n + 7 = 2n + 12

7n - 2n + 7 = 2n - 2n + 12

5n + 7 = 12

5n + 7 - 7 = 12 - 7

5n = 5

5n/5 = 5/5

n = 1

b.) 8n - ( 4 + 9 ) =11

8n - (4 + 9) = 11

8n - 13 = 11

8n - 13 + 13 = 11 + 13

8n = 24

8n/8 = 24/8

1n = 3

n = 3

c.) ( 8 - 3 )n + 7 n + 8 = 4n + 40

(8 - 3 )n + 7n + 8 = 4n + 40

5n + 7n + 8 = 4n + 40

12n + 8 = 4n + 40

12n - 4n + 8 = 4n - 4n + 40

8n + 8 = 40

8n + 8 - 8 = 40 - 8

8n = 32

8n/8 = 32n/8

n = 4

5. For this question you need to create a T-Chart and a graph to plot your data from this question onto.

You are having a race against your friend, except you are on foot and he is on his bike. You both know that if you are in your bike you will be faster so your friend gives you a head start of 3 minute. If you can run 400m per minute, and your friend can bike 700m per minute, who will be the first to make it to the finish line 2000m away?

t-chart :

graph :

you got to the finished line in 5 minutes while your friend got there in about 6 minutes. That means you won the race even though you run.

## 5 Comments:

how 'd u make a t-chart if u hav 3 things to put in it

One suggestion is put them in different colored lines or different styled line like dotted, dashed, or straight line

Rain your post is great, I really enjoyed your detailed explanations for expressions and equations. The only small problem is with 4c, I think that you made a small problem in your calculation as the answer is not n=3.

Fix this problem and your post is going into the hall of fame

oops i put 3 instead of 4

great work rainer. Your mark is 30/30

congrats

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