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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
Powers
Solving Quadratic Equations by Completing the Square
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Inequalities in one Variable

In this section we will learn how to use the relation symbols in word sentences and how to translate them into mathematical sentences.

Comparison Symbols

English terms; Relation Symbols and their Logical (negative) equivalents:
English Relation Negation (opposite)
equals = is, equals ≠ not equal (not an equivalent)
less than < is less than is not greater than or equal
at most ≤ is less than or equal is not greater than
beyond > is greater than is not less than or equal
at least ≥ is greater than or equal is not less than

Rules of Order of Operations

Please Pardon My Dear Aunt Sally

Parentheses (Grouping): Work from inside out.

Powers (Exponents): Simplify all powers first.

Multiply and/or

Divide: Work left to right (watch signs).

Add and/or Subtract: Combine like terms only.

 

Properties of Inequalities

For any real numbers a, b, and c:

1. EQUIVALENT PROPERTY:

a < b b > a

2. ADDITION PROPERTY:

If a < b is true then a + c < b + c is true.

3. MULTIPLICATION PROPERTY:

For c > 0, if a < b is true then a ·c < b ·c is true.

For c < 0, if a < b is true then a ·c > b ·c is true.

NOTE: Negation reverses every sign in its path. (-1)·(-2 < 3) +2 > -3

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