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GRE Review - Algebra

Objectives

• Students will be able to use the
multiplication and addition principles
together to solve linear equations

Solve for x :

3x – 2 = 10

3x = 12

x = 4

Example

3w + 4 = 5w − 6
Example

2(a − 3) = −5(2a +1)
Solving a system of linear equations
 
• Solve Be sure you pay attention to
what they are asking for.
Sometimes they may ask:
what is the value of x + y?
If this is the case, you would
just multiply the 2nd
equation by -1 and add; you
get x + y = 1.
Mult 2nd
eq. by -2
Add
Solving Quadratics
Example

Students will be able to

• Solve equations by factoring


 

Example

• If the quadratic does
not factor, we will use the quadratic
formula:

Inequalities
Example

Students should be able to

• solve linear inequalities

Double Inequalities

• They will sometimes stipulate some constraints on a
variable
.

0 < y < 1

• This should be read, y is greater than 0 and less than 1. In
other words, y is between and not including or 1). If it
had been:



Then we it is everything between 0 and 1 inclusive, that is y is
between 0 and 1inlcuding 0 and 1.

Applications

• It would be impossible to cover the
myriad of applications that could be on
the test. I will go through the thought
process on just one here.
Example

• Lex is twice as far from the finish line as
he is from the start of 18 mile race. How
far has he run?
Methodology

Step 1. Read the problem. If you don’t understand
it, read it again. If you still don’t understand it, read
it a 3rd time.

Step 2. Identify the given information

Step 3. Identify what you are trying to find.

Step 4. Draw a picture if necessary to help you
visualize the problem.

Step 5. Start labeling the drawing or setting up a
formula to solve .

Step 6. Solve the problem.

Step 7. Make sure your answer makes sense.
Example

• Lex is twice as far from the finish line as
he is from the start of 18 mile race. How
far has he run?

Coordinate Geometry
Example ( Plotting Points )

• Plot the following pairs of points
A (1, 3), B (-2, 3), C (-1, -2), D (0, 2).

Example

Students should be able to

• find the slope when given a line or
points on the line

Derivation of the slope formula

Example

• Find the slope of the line containing the
points (0,-1), (-5, 3)

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