6/05/2010 @ 8:12 PM
Equations
In this unit, you will learn about solving simple equations, multi-step equations, equations with fractions, and modeling with algebra/formulas.

Simple equations are usually straightforward, and not very hard.

TIP: Equations and expressions are NOT alike! 
Expression: a²b² + 3ab -1 
Equation: x² - 3xy = 2 


Equations have equal signs!


To "solve" means to find the value of the variables that makes the equation true. There are 2 ways of doing this, and the first way is solving by inspection.


Basically, what you do is solve for the missing variable- you can even eyeball the answer! (Eyeball- just look over and guess what the answer is- common sense)


EXAMPLE: x + 12 = 19 
                          x = 7


The second way of solving an equation is solving by isolation. This is the way most people take, since it lets you check your answers with a LS/RS check.


What you do is isolate the variable on one side of the equation by using opposite operations.


EXAMPLE:  y + 12 = 23 
                              y= 23 - 12
                              y= 11


TIP: Remember to do LS = RS check! For example:  y + 12 = 23, y = 11


SAMDEB
SAMDEB is actually BEDMAS backwards! Since we use opposite operations while solving equations, we use SAMDEB instead. 


To use it, you first get rid of the constant term on the same side of variable with subtraction/addition, then you isolate the variable by multiplying/dividing the coefficient.

We also learned how to solve multi-step equations. These equations usually have more than one variable, usually 2. What you do is collect the variable terms on one side, and the constant terms on the other side.

EXAMPLE: 13x – 5 = 10x + 7
                 13x - 10x = 7 + 5 
                             3x = 12
                          3x/3 = 12/3
                               x = 4


QUESTIONS: 
Solve each equation:
1) x + 6 = 2x – 8
ANSWER: 6 + 8 = 2x -x
        14 = x


2) 4(x – 2) = 12
ANSWER: 4x -8 = 12
                      4x  = 12 + 8
                       4x = 20 
                    4x/4 = 20/4
                         x = 5


36(2x – 5) = 4x + 2
ANSWER: 12x - 30 = 4x + 2
                 12x - 4x  = 2 + 30 
                          8x  = 32
                       8x/8  = 32/8
                           x   = 4

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Hello, my name is Sohyun Kim, and I am in grade 9. This site is for my math summative project, so no hateful comments please. I generally like to read, draw, read manga, and watch anime in my spare time.
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definitions.
Polynomials: Algebraic expressions made up of terms
Monomial: 1 term
Binomial: 2 terms
Trinomial: 3 terms
Terms: Made up of a coefficient and variable(s)
Power: Product of identical factors and consists of 2 parts- exponent and base. Coefficient: ----
Variable: ----
Constant/constant term: A term with no variable
Hypothesis: A theory or statement that is either true or false
Statistics: The collection, organization, and analysis of numerical data
Primary Data: Data that comes from experiments and surveys done by researchers
Secondary Data: Data that already exists- comes from sources such as the internet, magazines, and Statistics Canada
Interpolation: Prediction involving a point within the set of data
Extrapolation: Prediction involving a point outside the set of data
Linear Relation: Relation between 2 variables, forms a straight line
Non-Linear Relation: Relation between 2 variables, does NOT form a straight line
Curve of best fit: Curve that comes closest to the points of a non-linear relation
First Differences: -----
Slope: The steepness of a line- ratio of the rise to the run between both points
Direct Variation: A relationship between 2 variables in which one variable is a constant multiple of the other
Partial Variation: When a relationship between 2 variables have both a fixed and variable amount
Continued -HERE-

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