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Finding the Greatest Common Factor
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The FOIL Method
Graphing Compound Inequalities
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Factoring
Multiplication Properties of Exponents
Completing the Square
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Elimination Using Multiplication
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Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
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Multiplication by 111
Adding Fractions
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Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
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Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 
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Solving Linear Inequalities in One Variable

(vertically - using the balance beam )

Solve Equation with a Balance Beam

Pattern: ax + b cx + d

Both sides simplified (a ,b, c, d are integers.)

Look at the coefficients of x and determine which is the larger integer (furthest to the right on the number line). If c > a then we will keep the variiablle x on that siide of the equation and keep the constant on the other side. To do this we first add opposites on the balance beam below the equation. Look at the pattern, and then follow the same steps through several examples

Solve simplified equations vertically - using the balance beam.

Pattern: c > a

1) Add opps: c > a → c - a > 0
Complete the step: (b - d) ≥ (c - a)x Let A = (c - a) and B = (b - d)

A, B are integers, A > 0

2) Multiply recip:

Then:

Since and

A > 0 is coefficient of x

Equivalent Property

This means that all replacement values for x will be on or to the left of

NOTE: Since A > 0 all signs in its path remain the same. This is the advantage of choosing the side of larger coefficient when simplifying the problem.

 

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