## Thursday, March 21, 2013

### Ashlyn's Unproject

This is my proof that I know how to do algebra. 3 questions that I have created to show how I understand how to do 2 step algebra.
The first type of algebra equation that I will solve is a 2 step multiply. The equation that I have created is 9x - 10 = 53. Here's the solvation of Question 1.

9x - 10 = 53
You always start by writing the equation out as is before isolating the variable.
9x - 10 + 10 = 53 + 10
Time to start isolating the variable. You start with the constant (Definitions are at the end). Since you        performed an operation on one side, you have to reflect that action on the other side to make it equal.
9x = 63
Now you simplify the equation.
9x = 63
9       9
Dividing the first side by the coefficient (Definitions are at the end) will fully isolate the variable, and we balanced the equation by dividing by 9 (The coefficient).
x = 7
We have re - simplified the equation and have a value for x. But we are not done. We must verify (or prove) x = 7 in this equation.
9x - 10 = 53
You must always re write the equation first when verifying or it will count as incorrect (Believe me, I know).
9(7) - 10 = 53
Substitute your variable for the value you found, as you are testing to see if it is the correct value. You must put brackets around the substituted value, or it will look like 97, not 9x7.
63 - 10 = 53
First we multiply, just like in BEDMAS, because we need a value to subtract from, and if you try to subtract 10 from 9(7), the equation will be incorrect.
53 = 53
You have finished solving the equation and both sides are equal, so in this case, x = 7. This equation is solved, but we still have 2 more to solve.

Now we have to solve a 2 step divide, like this one.
y + 11 = 18
7
You must write out the equation before isolating the variable.
y
7 + 11 - 11 = 18 - 11
You must start by getting rid of the constant, by performing the opposite operation. To balance the equation, redo that action on the other side of the equal side.
y = 7
7
Now to simplify the equation as we go on and undo the coefficient.
7y = 7(7)
7
We multiply both sides by the coefficient, on the first side, the variable will be isolated, and on the other side, the same function is performed to balance the equation.
y = 49
We simplify the equation once again and have a value for the variable. But before we call it a wrap, we have to verify.
y+ 11 = 18
7
Don't forget to write out the equation first.
49 + 11 = 18
7
Now we substitute the variable and put it's new found value in its place to see if it is correct.
7 + 11 = 18
In BEDMAS, we always go with multiplication/division before addition/subtraction. When we are looking for the variable's value, we must do the reverse BEDMAS, or SAMDEB.
18 = 18
If both sides of the equation are equal, then you have correctly solved the equation. If not, re-read this and figure out where you went wrong.

There is still one more type of 2 step algebra equations that must be taught. It is called a distributive equation. Here's an example:
3(a - 40) = 150
There are 2 ways to solve an equation like this, but I'll do the one I find easier to do.
3(a - 40) = 150
Like every algebra equation, you must write out the question, then do the reverse BEDMAS.
3(a - 40) = 150
3                3
First we divide by 3, then we can work on the brackets.
a -40 = 50
Now it's time to simplify. Make sure you don't skip steps because you already solved it mentally, you should always follow through to be as accurate as possible.
a - 40 + 40 = 50 + 40
Now we undo the work of the constant by using its zero pair. Always perform the operation on both sides of the equation or it will not work when you verify.
a = 90
Equation solving is done, value of variable found, and all that's left to do for this equation is verification.
3(a - 40) = 150
Don't forget, like always, the equation has to be rewritten.
3(90 - 40) = 150
Substitute the variable for its value to check if it's the correct answer.
3(50) = 150
Solve the brackets first, before multiplying. Like most questions, verification requires you to perform BEDMAS, not SAMDEB.
150 = 150
You have properly solved the equation at hand if you have solved to equality.

You may have noticed some words in blue. What's up with that? Those are the words that must be defined.

variable: A letter in an algebra equation that represents an unknown value.
constant: A number that remains the same throughout the equation that is added or subtracted from the value of the variable.
coefficient: A number that is a multiplier to the variable.
verify: To check if the value found for the variable is the correct value in the equation.

If you still don't understand algebra, try to watch this video I found.

If not, then try to go on a good math website. Like this one.

http://www.freemathhelp.com/algebra-help.html