EQUATIONS AND INEQUALITIES
CHAPTER 1: POLYNOMIAL EQUATIONS AND INEQUALITIES
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A. EQUATIONS
1. Polynomial Equations
2. Linear Equations
3. Quadratic Equations
4. Higher Degree Equations
a. Higher Degree Equations
b. Factorization
c. Change of Variable
d. (OPTIONAL) Symmetric Equations
e. (OPTIONAL) Homogeneous Equations
5. Systems of Equations
a. Substitution
b. Combining Equations
c. Graphical Solution
d. (OPTIONAL) Decomposing The System
e. (OPTIONAL) Change of Variable
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B. INEQUALITIES
1. Linear Inequalities
2. Inequalities of Higher Degree
3. Systems of Inequalities
a. Systems with One Variable
b. (OPTIONAL) Systems with Two Variables
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CHAPTER 2: RATIONAL EQUATIONS AND INEQUALITIES
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A. EQUATIONS
1. Rational Equations
2. Systems of Equations
B. INEQUALITIES
1. Rational Inequalities
2. Systems of Inequalities
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CHAPTER 3: ABSOLUTE VALUE EQUATIONS AND INEQUALITIES
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A. EQUATIONS
1. The Definition of Absolute Value
2. Absolute Value Equations
a. Using Definition
b. (OPTIONAL) Graphical Solution
c. Squaring Both Sides of Equation
d. Dividing Into Cases
e. Change of Variable
3. Systems of Equations
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B. INEQUALITIES
1. Absolute Value Inequalities
2. Systems of Inequalities
CHAPTER 4: IRRATIONAL EQUATIONS AND INEQUALITIES
A. EQUATIONS
1. Irrational Equations
a. Raising Both Sides to the Same Power
b. Change of Variable
c. (OPTIONAL) Functional Approach or Using Graphs
2. Systems of Equations
B. INEQUALITIES
1. Irrational Inequalities .
2. (OPTIONAL) Systems of Inequalities
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CHAPTER 5: (OPTIONAL) EQUATIONS AND INEQUALITIES WITH PARAMETERS
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A. EQUATIONS
1. Finding Required Solutions With Respect To Parameter
a. Number of Solutions
b. Solutions That Satisfy Given Condition
2. Solving Equations In Terms of Parameter
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B. INEQUALITIES
1. Finding Required Solutions With Respect To Parameter
a. Existence of Solution
b. Solutions That Satisfy Given Condition
2. Solving Inequalities In Terms of Parameter