Chapter 3 Linear Equations and Inequalities Sect. 3.1 Solving Linear Equations Part I

The Addition and Subtraction Properties of Equality Ex. 1 Solve and check x - 8 = 3

Multiplication and Division Properties of Equality Ex. 2 Solve and check 4k = -24

Solve Equations of the Form ax + b = c Ex. 3 Solve 4/7 a - 5 = 1

Combine Like Terms on One Side of the Equal Sign and Solve Ex. 4 Solve 4x + 9 -6x + 2 = 17

Sect. 3.2 Solving Linear Equations Part II

How to Solve a Linear Equation

Example of Solving a Linear Equation

Example of Solving continued

Solve Equations Containing Fractions or Decimals Ex. 3

Fractional Equation Continued Ex. 4

Solving Equations that have No Solution or an Infinite Number of Solutions Ex. 5 Ex. 6

Outcomes When Solving Linear Equations

Solving Applied Problems

Example of Applied Problem Ex. 7 Six more than a number is nineteen. Find the number.

More examples of Applied problems

Sect. 3.3 Applications of Linear Equations to General Problems, Consecutive Integers, and Fixed and Variable Cost

Applied Problem continued

Solve Problems Involving Different Lengths Ex. 2 Solve Problems Involving Different Lengths

Length Problem continued

Consecutive Integer Problems To define the unknowns for consecutive integers, let Ex. 3

Consecutive Even and Consecutive Odd Integers

Consecutive Odd Problem continued

Solve Problems Involving Fixd and Variable Costs Ex. 5

Another Problem Using Fixed and Variable Costs

Problem Involving Fixed and Variable Costs continued

Applications of Linear Equations to Percent Increase/Decrease and Investment Problems Ex. 1

Problems Involving Percent Change Ex. 2 The sale price of a CD is 14.80 after a 20% discount. What was the original price of the CD?

Problems Involving Simple Interest Ex. 3

Another Simple Interest Problem Ex. 4

Another Simple Interest Problem Ex. 5

Simple Interest Problem continued Neema invested $4000 at 5% interest.

Sect. 3.5 Geometry Applications and Solving Formulas for a Specific Variable Ex. 1

Geometry example continued

Solve Problems Involving Angle Measures Ex. 2

Solve Problems Involving Complementary and Supplementary Angles Ex. 3

Angle example continued

Solve an Equation for a Specific Variable Ex. 4

Example of Solving for Specific Variable cont.

More examples of solving for a Specific Variable

More examples of solving for a Specific Variable

Sect. 3.6 Applications of Linear Equations to Proportion, d = rt, and Mixture Problems

Solve a Proportion Ex. 1 Ex. 2

Solve Problems Involving a Proportion Ex. 3 Solve Problems Involving a Proportion

Similar Triangles

Problem Involving Similar Triangles Ex. 4

Problems Involving Money

Another Problem Involving Money

Mixture Problems Ex. 7

Mixture Problems continued Ex. 8

Mixture Problems continued 30 - x =10 so 20 L of the 4% solution and 10 L of the 10% solution.

Rate, Time and Distance Problems The formula used in rate, time and distance problems is: distance = rate x time Ex. 9

Rate, Time and Distance Problems So 3.5 hours is the time Jenny has traveled and t - .5 = 3 hr = Alexandra’s time.

Sect. 3.7 Linear Inequalities in One Variable

Example of Linear Inequality Ex. 1 Graph the inequality x < -1 and express the solution in set notation and interval notation.

Solving Linear Inequalities

Example of Solving a Linear Inequality

Solve Linear Inequalities Using Multiplication Property

Example of Solving Using Multiplication Property Ex, 3 Solve -5w < 20 Graph the solution set and write the answer in interval and set notations.

Another example of Solving Inequalities

Solve Compound Inequalities with 3 Parts Ex. 5

Inequalities with Fractions

Another Example of a Compound Inequality

Applications Involving Linear Inequalities Ex. 8

Inequality Problem continued

Section 3.8 Compound Inequalities Union and Intersection of Sets Ex. 1

Solve Compound Inequalities Containing “And” Ex. 2

Compound Inequality Problem continued

Steps for Solving a Compound Inequality

Example of Compound Inequality

Example of Compound Inequality continued

Compound Inequalities Containing the word “or” Ex. 4 Compound Inequalities Containing the word “or”

Compound Inequalities that have No Solution or that have Solution Sets of All Real Numbers

Solve Special Compound Inequalities (cont.)