Section 2 1 The Addition Subtraction Properties of

Section 2. 1 The Addition & Subtraction Properties of Equality

OBJECTIV ES A Determine whether a number satisfies an equation.

OBJECTIV ES B Use the addition and subtraction properties of equality to solve equations.

OBJECTIV ES C Use both properties together to solve an equation.

SOLUTIONS The replacements of the variable that make the equation a true statement. “Solved the equation. ”

SOLUTIONS A number that is a solution of an equation satisfies the equation.

SOLUTIONS For example 3 is a solution of 2 x = 6 because: 3 satisfies the equation.

PROCEDURE: Solving Equations by Adding or Subtracting 1. Simplify both sides if necessary.

PROCEDURE: Solving Equations by Adding or Subtracting 2. Add or subtract the same numbers on both sides so that one side contains only variables.

PROCEDURE: Solving Equations by Adding or Subtracting 3. Add or subtract the same expressions on both sides so that the other side contains only numbers.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #1

Yes.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #2

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #3

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #4

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #5

Impossible. No solution.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 1 Exercise #6

All real numbers.

Section 2. 2 The Multiplication and Division Properties of Equality

OBJECTIV ES A Use the multiplication and division properties of equality to solve equations.

OBJECTIV ES B Multiply by reciprocals to solve equations.

OBJECTIV ES C Multiply by LCMs to solve equations.

OBJECTIV ES D Solve applications involving percents.

PROCEDURE: Clearing Fractions Multiply both sides of the equation by the LCM of the denominators. Or, multiply each term by the LCM.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #7

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #8

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #9

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #10

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #11

LCD = 40

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #12

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 2 Exercise #13

Section 2. 3 Linear Equations

OBJECTIV ES A Solve linear equations in one variable.

OBJECTIV ES B Solve a literal equation for one of the unknowns.

PROCEDURE: Solving Linear Equations 1. Clear fractions (Multiply by the LCM of the denominator).

PROCEDURE: Solving Linear Equations

PROCEDURE: Solving Linear Equations 2. Remove parentheses and simplify.

PROCEDURE: Solving Linear Equations 3. Isolate the variable.

PROCEDURE: Solving Linear Equations

PROCEDURE: Solving Linear Equations 4. If coefficient is NOT 1, divide both sides by coefficient

PROCEDURE: Solving Linear Equations

PROCEDURE: Solving Linear Equations 5. Check your answer in the original equation.

PROCEDURE: Solving Linear Equations

Literal Equation An equation that contains several variables.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 3

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 3 Exercise #14

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 3 Exercise #15

Section 2. 4 Problem Solving: Integer, General, and Geometry Problems

OBJECTIV Use RSTUV method to solve ES A Integer problems B General word problems Geometry word problems C

PROCEDURE: RSTUV Method for Solving Word Problems 1. Read the problem and decide what is asked for (the unknown).

PROCEDURE: RSTUV Method for Solving Word Problems 2. Select a variable to represent this unknown.

PROCEDURE: RSTUV Method for Solving Word Problems 3. Think of a plan to help you write an equation.

PROCEDURE: RSTUV Method for Solving Word Problems 4. Use algebra to solve the resulting equation.

PROCEDURE: RSTUV Method for Solving Word Problems 5. Verify the answer.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 4 Exercise #16

The numbers are 30 and 45.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 4 Exercise #17

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 4 Exercise #18

Section 2. 5 Problem Solving: Motion, Mixture, and Investment Problems

OBJECTIV Use the RSTUV method to s ES A Motion problems B Mixture problems C Investment problems

PROCEDURE: RSTUV Method for Solving Word Problems 1. Read the problem and decide what is asked for (the unknown).

PROCEDURE: RSTUV Method for Solving Word Problems 2. Select a variable to represent this unknown.

PROCEDURE: RSTUV Method for Solving Word Problems 3. Think of a plan to help you write an equation.

PROCEDURE: RSTUV Method for Solving Word Problems 4. Use algebra to solve the resulting equation.

PROCEDURE: RSTUV Method for Solving Word Problems 5. Verify the answer.

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 5 Exercise #19

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 5 Exercise #21

I= RT

I= RT

Section 2. 6 Formulas and Geometry Applications

OBJECTIV ES A Solve a formula for one variable and use the result to solve a problem.

OBJECTIV ES B Solve problems involving geometric formulas.

OBJECTIV ES C Solve geometric problems involving angle measurement.

OBJECTIV ES D Solve an application.

DEFINITION

DEFINITION Complementary Angles are called complementary angles.

DEFINITION Complementary Angles

DEFINITION Supplementary Angles are called supplementary angles.

DEFINITION Supplementary Angles

DEFINITION Vertical Angles

DEFINITION Vertical Angles 1 2 4 3

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 6

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 6 Exercise #22

Section 2. 7 Properties of Inequalities

OBJECTIV ES A Determine which of two numbers is greater.

OBJECTIV ES B Solve and graph linear inequalities.

OBJECTIV ES C Write, solve, and graph a compound inequality.

OBJECTIV ES D Solve an application.

DEFINITIONS On the number line, greater numbers are always to the right of smaller ones. – 3 – 2 – 1 0 1 2 3 > 1 or 1 < 3 3

DEFINITIONS Addition and Subtraction Properties of Inequalities. You can add or subtract the same number on both sides of an inequality and obtain an equivalent inequality.

DEFINITIONS Addition and Subtraction Properties of Inequalities.

DEFINITIONS Addition and Subtraction Properties of Inequalities.

DEFINITIONS Multiplication and Division Properties of Inequalities for Positive You can multiply or Numbers divide both sides of an inequality by any positive number and obtain an

DEFINITIONS Multiplication and Division Properties of Inequalities for Positive Numbers

DEFINITIONS Multiplication and Division Properties of Inequalities for Positive Numbers

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 7

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 7 Exercise #24

Chapter 2 Equations, Problem Solving, and Inequalities Section 2. 7 Exercise #25

Solve and graph the inequality. LCD = 4

Solve and graph the inequality.

Solve and graph the inequality.