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	Elimination Using Multiplication
	Prime Factors
	Equations Involving Rational Exponents
	Working with Percentages and Proportions
	Rational Expressions
	Interval Notation and Graphs
	Simplifying Complex Fractions
	Dividing Whole Numbers with Long Division
	Solving Compound Linear Inequalities
	Raising a Quotient to a Power
	Solving Rational Equations
	Solving Inequalities
	Adding with Negative Numbers
	Quadratic Inequalities
	Dividing Monomials
	Using the Discriminant in Factoring
	Solving Equations by Factoring
	Subtracting Polynomials
	Cube Root
	The Quadratic Formula
	Multiply by the Reciprocal
	Relating Equations and Graphs for Quadratic Functions
	Multiplying a Polynomial by a Monomial
	Calculating Percentages
	Solving Systems of Equations using Substitution
	Comparing Fractions
	Solving Equations Containing Rational Expressions
	Factoring Polynomials
	Negative Rational Exponents
	Roots and Radicals
	Intercepts Given Ordered Pairs and Lines
	Factoring Polynomials
	Solving Linear Inequalities
	Powers
	Mixed Expressions and Complex Fractions
	Solving Equations by Multiplying or Dividing
	The Addition Method
	Finding the Equation of an Inverse Function
	Solving Compound Linear Inequalities
	Multiplying and Dividing With Square Roots
	Exponents and Their Properties
	Equations as Functions
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	Factoring Trinomials
	Solving Quadratic Equations by Completing the Square
	Dividing by Decimals
	Lines and Equations
	Simplifying Complex Fractions
	Graphing Solution Sets for Inequalities
	Standard Form for the Equation of a Line
	Fractions
	Checking Division with Multiplication
	Elimination Using Addition and Subtraction
	Complex Fractions
	Multiplication Property of Equality
	Solving Proportions Using Cross Multiplication
	Product and Quotient of Functions
	Adding
	Quadratic Functions
	Conjugates
	Factoring
	Solving Compound Inequalities
	Operating with Complex Numbers
	Equivalent Fractions
	Changing Improper Fractions to Mixed Numbers
	Multiplying by a Monomial
	Solving Linear Equations and Inequalities Graphically
	Dividing Polynomials by Monomials
	Multiplying Cube Roots
	Operations with Monomials
	Properties of Exponents
	Percents
	Arithmetics
	Mixed Numbers and Improper Fractions
	Equations Quadratic in Form
	Simplifying Square Roots That Contain Whole Numbers
	Dividing a Polynomial by a Monomial
	Writing Numbers in Scientific Notation
	Solutions to Linear Equations in Two Variables
	Solving Linear Inequalities
	Multiplying Two Mixed Numbers with the Same Fraction
	Special Fractions
	Solving a Quadratic Inequality
	Parent and Family Graphs
	Solving Equations with a Fractional Exponent
	Evaluating Trigonometric Functions
	Solving Equations Involving Rational Expressions
	Polynomials
	Laws of Exponents
	Multiplying Polynomials
	Vertical Line Test
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	Solving Inequalities with Fractions and Parentheses
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	Multiplying Polynomials
	Fractions
	Solving Quadratic and Polynomial Equations
	Extraneous Solutions
	Fractions

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Multiplication Property of Equality

General equation: Ax + B = C x + D (A, B, C, D are real numbers.).

More often the equations have constants that are a mixture of fractions and integers. Generally, it is better to multiply the equation by the LCD to clear the fractions.

i) Simplify the equation so that there are only integers on both sides

ii) Then solve simplified equations vertically - using the balance beam.

Example 1:

Solve
Multiply LCD:

Solve vertically:

Add Opps:
Check:

General equation: Ax + B = C x + D (A, B, C, D are rational numbers.).

i) Simplify the equation so that there are only integers on both sides

ii) Then solve simplified equations vertically - using the balance beam.

Example 2:

Solve
Multiply LCD:

Solve vertically:
1) Add Opps:
Complete the step:
2) Multiply recip:	Since
Then
Check:		Note that is correct.

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