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**Equations and Inequalities**

College Algebra Chapter 1 Equations and Inequalities

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**Solving equations using **

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Solving equations using Addition and multiplication properties of equality

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**Solving equations using **

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Solving equations using Addition and multiplication properties of equality General Approach Simplify the equation Clear fractions or decimals as needed/desired Combine any like terms Solve the equation Use additive property of equality to write the equation with all variable terms on one side and constants on the other Simplify each side Use the multiplicative property of equality to obtain solution form

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**Solving equations using **

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Solving equations using Addition and multiplication properties of equality General Approach Simplify the equation Clear fractions or decimals as needed/desired Combine any like terms Solve the equation Use additive property of equality to write the equation with all variable terms on one side and constants on the other Simplify each side Use the multiplicative property of equality to obtain solution form

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**Solving equations using **

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Solving equations using Addition and multiplication properties of equality General Approach Simplify the equation Clear fractions or decimals as needed/desired Combine any like terms Solve the equation Use additive property of equality to write the equation with all variable terms on one side and constants on the other Simplify each side Use the multiplicative property of equality to obtain solution form

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**Linear Equation Terminology**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Linear Equation Terminology Algebraic expression Equation Linear equations Standard form Conditional equation Identity Contradictions Sum or difference of algebraic terms Statement that two expressions are equal Three tests – exponents, divisors, multiplication Ax+By=C, where A and B are not both zero Equation is true for one value and false for all others Equation that is always true Equations that are never true

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving No Solution

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

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**Linear Equation Terminology**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Linear Equation Terminology Literal equation Formula An equation that has two or more unknowns Equation that models a known relationship between two or more quantities

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Literal Equations:

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Literal Equations:

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**Consecutive Integer Problems**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Consecutive Integer Problems Sum of 3 even integers is 66. What are they?

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Mixture Problems

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Mixture Problems

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

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**College Algebra Chapter 1**

College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving Homework pg

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**Inequalities and Solution Sets Terminology**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Inequalities and Solution Sets Terminology Solution Set Set Notation Number Line Interval Notation Boundary Point Inclusion Not Included The set of numbers that satisfy an inequality Method of writing a solution set. Ex {x|x>k} Method of writing a solution set Method of writing a solution set. Ex Marks the location of a number on a number line also called an endpoint Uses brackets [ ] to indicate Uses parenthesis ( ) to indicate

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**Inequalities and Solution Sets Terminology**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Inequalities and Solution Sets Terminology Set Notation The set of all n Such that n is greater than or equal to 1

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**Inequalities and Solution Sets Terminology**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Inequalities and Solution Sets Terminology Interval Notation n is an element of This set Smaller number to left Larger number to right [,] brackets if boundary points is included (,) parenthesis if boundary point is not included

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**Write the following in set notation, number line graph, **

College Algebra Chapter 1.2 Linear Inequalities in One Variable Write the following in set notation, number line graph, and interval notation x is less than 10 Set notation Number line graph 10 Interval notation

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**Write the following in set notation, number line graph, **

College Algebra Chapter 1.2 Linear Inequalities in One Variable Write the following in set notation, number line graph, and interval notation n is greater than or equal to 2 Set notation Number line graph 2 Interval notation

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**Write the following in set notation, number line graph, **

College Algebra Chapter 1.2 Linear Inequalities in One Variable Write the following in set notation, number line graph, and interval notation X is less than 5 and greater than or equal to -1 Set notation Number line graph -1 5 Interval notation

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**Solving Inequalities Beware of multiplying or dividing by a (-)**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Solving Inequalities Beware of multiplying or dividing by a (-)

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**College Algebra Chapter 1.2 Linear Inequalities in One Variable**

Solving Inequalities

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**Solving Compound Inequalities**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Solving Compound Inequalities

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**Solving Compound Inequalities**

College Algebra Chapter 1.2 Linear Inequalities in One Variable Solving Compound Inequalities

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**College Algebra Chapter 1.2 Linear Inequalities in One Variable**

Homework pg

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

Zero factor property Given that A and B represent real numbers or real-valued expressions, if , then either

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**Remove common factors aka undistribute**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solve Set equal to zero Remove common factors aka undistribute Factor trinomial Solve each factor equal to zero

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

Solve

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

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**Solving rational equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving rational equations Identify and exclude values that cause a zero denominator Multiply by the LCD and simplify Solve resulting equation Check in original equation and step 1

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**Solving rational equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving rational equations Identify and exclude values that cause a zero denominator Multiply by the LCD and simplify Solve resulting equation Check in original equation and step 1

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**Solving rational equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving rational equations Identify and exclude values that cause a zero denominator Multiply by the LCD and simplify Solve resulting equation Check in original equation and step 1

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**Solving rational equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving rational equations Identify and exclude values that cause a zero denominator Multiply by the LCD and simplify Solve resulting equation Check in original equation and step 1

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**Solving rational equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving rational equations Identify and exclude values that cause a zero denominator Multiply by the LCD and simplify Solve resulting equation Check in original equation and step 1

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**Solving Radical Equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving Radical Equations Isolate radical term Square both sides Simplify

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**3 Solving Radical Equations Isolate radical term Square both sides**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving Radical Equations Isolate radical term Square both sides Simplify 3

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**Solving Radical Equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving Radical Equations Isolate radical term Square both sides Simplify

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**Solving Radical Equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving Radical Equations Isolate radical term Square both sides Simplify

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**Solving Radical Equations**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving Radical Equations Isolate radical term Square both sides Simplify

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

Rational Exponents 15

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

Rational Exponents

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**Solving with U-Substitution**

College Algebra Chapter 1.3 Solving Polynomial and Other Equations Solving with U-Substitution

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**College Algebra Chapter 1.3 Solving Polynomial and Other Equations**

Homework pg

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**Imaginary unit i represents the number whose square is -1**

College Algebra Chapter 1.4 Complex Numbers Imaginary unit i represents the number whose square is -1

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**College Algebra Chapter 1.4 Complex Numbers**

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**College Algebra Chapter 1.4 Complex Numbers**

Complex numbers are those that can be written in the form , where a and b are real numbers and The expression is called the standard form of a complex numbers Real part Imaginary part

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**Identify the values of a and b**

College Algebra Chapter 1.4 Complex Numbers Identify the values of a and b a=-5 b=3 -5+3i 2-3i a=2 b=-3 a=2 b=7 a=0 b= a=7 b=0 7

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**Identify the values of a and b**

College Algebra Chapter 1.4 Complex Numbers Identify the values of a and b a=0.2 b=0.75

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**Adding and subtracting complex numbers**

College Algebra Chapter 1.4 Complex Numbers Adding and subtracting complex numbers

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**Adding and subtracting complex numbers**

College Algebra Chapter 1.4 Complex Numbers Adding and subtracting complex numbers

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**Multiplying Complex Numbers**

College Algebra Chapter 1.4 Complex Numbers Multiplying Complex Numbers

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**Multiplying Complex Numbers**

College Algebra Chapter 1.4 Complex Numbers Multiplying Complex Numbers

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**Multiplying by the Complex Conjugate**

College Algebra Chapter 1.4 Complex Numbers Multiplying by the Complex Conjugate

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**Division of Complex Numbers**

College Algebra Chapter 1.4 Complex Numbers Division of Complex Numbers

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**College Algebra Chapter 1.4 Complex Numbers**

Homework pg

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**Standard Form and Coefficients**

College Algebra Chapter 1.5 Non-factorable Quadratic Equations Standard Form and Coefficients a=2 b=0 c=-10 a=-3 b=1 c=-12 a= b= c=0 Not quadratic

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**College Algebra Chapter 1.5 Non-factorable Quadratic Equations**

Square root property

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**College Algebra Chapter 1.5 Non-factorable Quadratic Equations**

solve

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**College Algebra Chapter 1.5 Non-factorable Quadratic Equations**

solve

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**Completing the Square Subtract the constant c from both sides**

College Algebra Chapter 1.5 Non-factorable Quadratic Equations Completing the Square Subtract the constant c from both sides Divide both sides by the leading coefficient a Take and add the result to both sides Factor the left hand side as a binomial square: simplify the right hand side Solve using the SQR property of equality

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**College Algebra Chapter 1.5 Non-factorable Quadratic Equations**

Completing the Square Subtract the constant c from both sides Divide both sides by the leading coefficient a Take and add the result to both sides Factor the left hand side as a binomial square: simplify the right hand side Solve using the SQR property of equality

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**Quadratic Formula Discriminant 1 real root 2 real roots**

College Algebra Chapter 1.5 Non-factorable Quadratic Equations Quadratic Formula Discriminant 1 real root 2 real roots 2 complex roots

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**Quadratic Formula Solve No Solution**

College Algebra Chapter 1.5 Non-factorable Quadratic Equations Quadratic Formula Solve No Solution

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**Quadratic Formula Solve {6,-3} {6,1}**

College Algebra Chapter 1.5 Non-factorable Quadratic Equations Quadratic Formula Solve {6,-3} {6,1}

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**College Algebra Chapter 1.5 Non-factorable Quadratic Equations**

Homework pg

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**Solve -10 No Solution All Real Numbers 2**

College Algebra Chapter 1 Review Solve -10 No Solution All Real Numbers 2

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**Solve and graph, state solution in set and interval notation**

College Algebra Chapter 1 Review Solve and graph, state solution in set and interval notation

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**Solve by the method of your choice**

College Algebra Chapter 1 Review Solve by the method of your choice {5, -5} {7.483, } {5/8, -8/5} {2/7, -7} {8, 7} {-4, 6} {0.732, } No solution {1.309, } {12.426, }

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**College Algebra Chapter 1 Review**

Solve {6} {3} {-1} {9, 2}

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**College Algebra Chapter 1 Review**

Homework pg

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