The Addition

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Section 2.1
The Addition Subtraction Properties of
Equality
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OBJECTIVES
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OBJECTIVES
Use the addition and subtraction properties of
equality to solve equations.
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OBJECTIVES
Use both properties together to solve an equation.
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SOLUTIONS
The replacements of the variable that make the
equation a true statement.
Solved the equation.
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SOLUTIONS
A number that is a solution of an equation
satisfies the equation.
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SOLUTIONS
For example
3 is a solution of 2x 6 because
3 satisfies the equation.
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PROCEDURE
Solving Equations by Adding or Subtracting
1. Simplify both sides if necessary.
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PROCEDURE
Solving Equations by Adding or Subtracting
2. Add or subtract the same numbers on both sides
so that one side contains only variables.
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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.
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Section 2.1Exercise 1
Chapter 2 Equations, Problem Solving, and
Inequalities
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Yes.
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Section 2.1Exercise 2
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.1Exercise 3
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.1Exercise 4
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.1Exercise 5
Chapter 2 Equations, Problem Solving, and
Inequalities
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Impossible. No solution.
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Section 2.1Exercise 6
Chapter 2 Equations, Problem Solving, and
Inequalities
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All real numbers.
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Section 2.2
The Multiplication and Division Properties of
Equality
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OBJECTIVES
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OBJECTIVES
Multiply by reciprocals to solve equations.
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OBJECTIVES
Multiply by LCMs to solve equations.
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OBJECTIVES
Solve applications involving percents.
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PROCEDURE
Clearing Fractions
Multiply both sides of the equation by the LCM of
the denominators.
Or, multiply each term by the LCM.
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Section 2.2Exercise 7
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 8
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 9
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 10
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 11
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 12
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.2Exercise 13
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.3
Linear Equations
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OBJECTIVES
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OBJECTIVES
Solve a literal equation for one of the unknowns.
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PROCEDURE
Solving Linear Equations
1. Clear fractions (Multiply by the LCM of the
denominator).
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PROCEDURE
Solving Linear Equations
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PROCEDURE
Solving Linear Equations
2. Remove parentheses and simplify.
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PROCEDURE
Solving Linear Equations
3. Isolate the variable.
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PROCEDURE
Solving Linear Equations
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PROCEDURE
Solving Linear Equations
4. If coefficient is NOT 1, divide both sides by
coefficient
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PROCEDURE
Solving Linear Equations
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PROCEDURE
Solving Linear Equations
5. Check your answer in the original equation.
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PROCEDURE
Solving Linear Equations
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Literal Equation
An equation that contains several variables.
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Section 2.3
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.3Exercise 14
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.3Exercise 15
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.4
Problem Solving Integer, General, and Geometry
Problems
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OBJECTIVES
Use RSTUV method to solve
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PROCEDURE
RSTUV Method for Solving Word Problems
1. Read the problem and decide what is asked for
(the unknown).
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PROCEDURE
RSTUV Method for Solving Word Problems
2. Select a variable to represent this unknown.
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PROCEDURE
RSTUV Method for Solving Word Problems
3. Think of a plan to help you write an equation.
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PROCEDURE
RSTUV Method for Solving Word Problems
4. Use algebra to solve the resulting equation.
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PROCEDURE
RSTUV Method for Solving Word Problems
5. Verify the answer.
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Section 2.4Exercise 16
Chapter 2 Equations, Problem Solving, and
Inequalities
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The numbers are 30 and 45.
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Section 2.4Exercise 17
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.4Exercise 18
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.5
Problem Solving Motion, Mixture, and Investment
Problems
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OBJECTIVES
Use the RSTUV method to solve
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PROCEDURE
RSTUV Method for Solving Word Problems
1. Read the problem and decide what is asked for
(the unknown).
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PROCEDURE
RSTUV Method for Solving Word Problems
2. Select a variable to represent this unknown.
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PROCEDURE
RSTUV Method for Solving Word Problems
3. Think of a plan to help you write an equation.
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PROCEDURE
RSTUV Method for Solving Word Problems
4. Use algebra to solve the resulting equation.
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PROCEDURE
RSTUV Method for Solving Word Problems
5. Verify the answer.
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Section 2.5Exercise 19
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.5Exercise 21
Chapter 2 Equations, Problem Solving, and
Inequalities
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I RT
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I RT
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Section 2.6
Formulas and Geometry Applications
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITION
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DEFINITION
Complementary Angles
are called complementary angles.
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DEFINITION
Complementary Angles
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DEFINITION
Supplementary Angles
are called supplementary angles.
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DEFINITION
Supplementary Angles
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DEFINITION
Vertical Angles
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DEFINITION
Vertical Angles
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Section 2.6
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.6Exercise 22
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.7
Properties of Inequalities
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITIONS
On the number line, greater numbers are always to
the right of smaller ones.
3 gt 1 or 1 lt 3
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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.
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DEFINITIONS
Addition and Subtraction Properties of
Inequalities.
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DEFINITIONS
Addition and Subtraction Properties of
Inequalities.
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DEFINITIONS
Multiplication and Division Properties of
Inequalities for Positive Numbers
You can multiply or divide both sides of an
inequality by any positive number and obtain an
equivalent inequality.
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DEFINITIONS
Multiplication and Division Properties of
Inequalities for Positive Numbers
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DEFINITIONS
Multiplication and Division Properties of
Inequalities for Positive Numbers
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Section 2.7
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.7Exercise 24
Chapter 2 Equations, Problem Solving, and
Inequalities
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Section 2.7Exercise 25
Chapter 2 Equations, Problem Solving, and
Inequalities
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Solve and graph the inequality.
LCD 4
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Solve and graph the inequality.
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Solve and graph the inequality.