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Chapter 3 Linear Equations and Inequalities
Sect. 3.1 Solving Linear Equations Part I
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The Addition and Subtraction Properties of Equality
Ex. 1 Solve and check x - 8 = 3
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Multiplication and Division Properties of Equality
Ex. 2 Solve and check 4k = -24
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Solve Equations of the Form ax + b = c
Ex. 3 Solve 4/7 a - 5 = 1
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Combine Like Terms on One Side of the Equal Sign and Solve
Ex. 4 Solve 4x x + 2 = 17
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Sect. 3.2 Solving Linear Equations Part II
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How to Solve a Linear Equation
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Example of Solving a Linear Equation
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Example of Solving continued
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Solve Equations Containing Fractions or Decimals
Ex. 3
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Fractional Equation Continued
Ex. 4
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Solving Equations that have No Solution or an Infinite Number of Solutions
Ex. 5 Ex. 6
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Outcomes When Solving Linear Equations
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Solving Applied Problems
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Example of Applied Problem
Ex. 7 Six more than a number is nineteen. Find the number.
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More examples of Applied problems
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Sect. 3.3 Applications of Linear Equations to General Problems, Consecutive Integers, and Fixed and Variable Cost
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Applied Problem continued
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Solve Problems Involving Different Lengths
Ex. 2 Solve Problems Involving Different Lengths
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Length Problem continued
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Consecutive Integer Problems
To define the unknowns for consecutive integers, let Ex. 3
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Consecutive Even and Consecutive Odd Integers
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Consecutive Odd Problem continued
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Solve Problems Involving Fixd and Variable Costs
Ex. 5
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Another Problem Using Fixed and Variable Costs
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Problem Involving Fixed and Variable Costs continued
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Applications of Linear Equations to Percent Increase/Decrease and Investment Problems
Ex. 1
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Problems Involving Percent Change
Ex. 2 The sale price of a CD is after a 20% discount. What was the original price of the CD?
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Problems Involving Simple Interest
Ex. 3
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Another Simple Interest Problem
Ex. 4
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Another Simple Interest Problem
Ex. 5
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Simple Interest Problem continued
Neema invested $4000 at 5% interest.
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Sect. 3.5 Geometry Applications and Solving Formulas for a Specific Variable
Ex. 1
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Geometry example continued
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Solve Problems Involving Angle Measures
Ex. 2
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Solve Problems Involving Complementary and Supplementary Angles
Ex. 3
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Angle example continued
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Solve an Equation for a Specific Variable
Ex. 4
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Example of Solving for Specific Variable cont.
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More examples of solving for a Specific Variable
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More examples of solving for a Specific Variable
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Sect. 3.6 Applications of Linear Equations to Proportion, d = rt, and Mixture Problems
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Solve a Proportion Ex. 1 Ex. 2
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Solve Problems Involving a Proportion
Ex. 3 Solve Problems Involving a Proportion
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Similar Triangles
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Problem Involving Similar Triangles
Ex. 4
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Problems Involving Money
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Another Problem Involving Money
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Mixture Problems Ex. 7
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Mixture Problems continued
Ex. 8
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Mixture Problems continued
30 - x =10 so 20 L of the 4% solution and 10 L of the 10% solution.
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Rate, Time and Distance Problems
The formula used in rate, time and distance problems is: distance = rate x time Ex. 9
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Rate, Time and Distance Problems
So 3.5 hours is the time Jenny has traveled and t - .5 = 3 hr = Alexandra’s time.
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Sect. 3.7 Linear Inequalities in One Variable
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Example of Linear Inequality
Ex. 1 Graph the inequality x < -1 and express the solution in set notation and interval notation.
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Solving Linear Inequalities
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Example of Solving a Linear Inequality
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Solve Linear Inequalities Using Multiplication Property
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Example of Solving Using Multiplication Property
Ex, 3 Solve -5w < 20 Graph the solution set and write the answer in interval and set notations.
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Another example of Solving Inequalities
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Solve Compound Inequalities with 3 Parts
Ex. 5
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Inequalities with Fractions
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Another Example of a Compound Inequality
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Applications Involving Linear Inequalities
Ex. 8
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Inequality Problem continued
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Section 3.8 Compound Inequalities
Union and Intersection of Sets Ex. 1
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Solve Compound Inequalities Containing “And”
Ex. 2
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Compound Inequality Problem continued
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Steps for Solving a Compound Inequality
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Example of Compound Inequality
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Example of Compound Inequality continued
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Compound Inequalities Containing the word “or”
Ex. 4 Compound Inequalities Containing the word “or”
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Compound Inequalities that have No Solution or that have Solution Sets of All Real Numbers
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Solve Special Compound Inequalities (cont.)
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