Section 2.1 Linear Equations in One Variable

OBJECTIVES A Determine whether a number is a solution of a given equation.

OBJECTIVES B Solve linear equations using the properties of equality.

OBJECTIVES C Solve linear equations in one variable using the six-step procedure(CRAM).

OBJECTIVES D Solve linear equations involving decimals.

DEFINITION For real numbers a, b, and c. PROPERTIES OF EQUALITIES 1.a = a Reflexive 2.If a = b, then b = a Symmetric 3.If a = b and b = c, then a = c Transitive

DEFINITION An equation that can be written in the form: LINEAR EQUATIONS

DEFINITION Replacements of the variable that make the equation a true statement. SOLUTIONS OF AN EQUATION

DEFINITION Two equations that have the same solution set. EQUIVALENT EQUATIONS

Clear fractions/decimals Remove parentheses/simplify Add/Subtract to get variable isolated Multiply/Divide to make coefficient 1 PROCEDURE

DEFINITION No solutions(contradictions): EQUATIONS WITH NO SOLUTIONS AND INFINITELY MANY SOLUTIONS Infinitely many solutions(identities):

Section 2.1 Exercise #5 Chapter 2 Linear Equations and Inequalities

Section 2.1 Exercise #6 Chapter 2 Linear Equations and Inequalities

Section 2.2 Formulas, Geometry and Problem Solving

OBJECTIVES A Solve a formula for a specified variable and then evaluate the answer for given values of the variables.

OBJECTIVES B Write a formula for a given situation that has been described in words.

OBJECTIVES C Solve problems about angle measures.

SOLVE FOR A SPECIFIED VALUE PROCEDURE 1.Add or Subtract the same quantity on both sides. 2.Use the distributive property. 3.Use CRAM.

Section 2.2 Chapter 2 Linear Equations and Inequalities

Section 2.2 Exercise #7 Chapter 2 Linear Equations and Inequalities

a. Solve for h.

Section 2.2 Exercise #9 Chapter 2 Linear Equations and Inequalities

a. Solve for L. b. If the perimeter is 100 ft and the length is 20 ft more than the width, what are the dimensions of the rectangle?

a. Solve for L.

b. If the perimeter is 100 ft and the length is 20 ft more than the width, what are the dimensions of the rectangle?

Section 2.2 Exercise #10 Chapter 2 Linear Equations and Inequalities

These are the alternate exterior angles and they are equal.

Section 2.3 Problem Solving: Integers and Geometry

OBJECTIVES A Translate a word expression into a mathematical expression.

OBJECTIVES B Solve word problems of a general nature.

OBJECTIVES C Solve word problems about integers.

OBJECTIVES D Solve word problems about geometric formulas and angles.

PROCEDURE: Read Select Think Use Verify RSTUV Method for Solving Word Problems

Section 2.3 Chapter 2 Linear Equations and Inequalities

Section 2.3 Exercise #11 Chapter 2 Linear Equations and Inequalities

The bill for repairing an appliance totaled $ If the repair shop charges $35 for the service call, plus $25 for each hour of labor, how many hours labor did the repair take?

Section 2.4 Problem Solving: Percent, Investment, Motion, and Mixture Problems

OBJECTIVES A Solve percent problems.

OBJECTIVES B Solve investment problems.

OBJECTIVES C Solve uniform motion problems.

OBJECTIVES D Solve mixture problems.

PROCEDURE: Read Select Think Use Verify RSTUV Method for Solving Word Problems

Section 2.4 Chapter 2 Linear Equations and Inequalities

Section 2.4 Exercise #14 Chapter 2 Linear Equations and Inequalities

An investor bought some municipal bonds yielding 5 percent annually and some certificates of deposit yielding 7 percent. If his total investment amounts to $20,000 and his annual interest is $1100, how much money is invested in bonds and how much in certificates of deposit?

Section 2.4 Exercise #15 Chapter 2 Linear Equations and Inequalities

A freight train leaves a station traveling at 40 mi/hr. Two hours later, a passenger train leaves the same station traveling in the same direction at 60 mi/hr. How far from the station does the passenger train overtake the freight train? Rate Time Distance Freight Passenger

Rate Time Distance Freight Passenger Their distances are equal:

Rate Time Distance Freight Passenger Their distances are equal: The passenger train overtakes the freight train 240 miles from the station.

Section 2.5 Linear and Compound Inequalities

OBJECTIVES A Graph linear inequalities.

OBJECTIVES B Solve and graph linear inequalities.

OBJECTIVES C Solve and graph compound inequalities.

OBJECTIVES D Use the inequality symbols to translate sentences into inequalities.

DEFINITION An inequality that can be written in the form: LINEAR INEQUALITIES

DEFINITION UNION OF TWO SETS

DEFINITION INTERSECTION OF TWO SETS

DEFINITION EQUIVALENT STATEMENTS FOR “AND”

Section 2.5 Chapter 2 Linear Equations and Inequalities

Section 2.5 Exercise #18 Chapter 2 Linear Equations and Inequalities

LCD = 24

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Section 2.5 Exercise #19 Chapter 2 Linear Equations and Inequalities

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Section 2.5 Exercise #20 Chapter 2 Linear Equations and Inequalities

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Section 2.5 Exercise #21 Chapter 2 Linear Equations and Inequalities

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Section 2.6 Absolute-Value Equations and Inequality

OBJECTIVES A Solve absolute-value equations.

OBJECTIVES B Solve absolute-value inequalities of the form |ax + b| c, where c > 0.

DEFINITION If a ≥ 0, the solutions of |x| = a are x = a and x = –a. THE SOLUTIONS OF |X| = A (A ≥ 0)

STATEMENT TRANSLATION If |expression| = a, where a ≥ 0 expression = a or –a ABSOLUTE VALUE EQUATIONS

STATEMENT TRANSLATION If |expression| = |expression|, expression = expression expression = – ( expression ) ABSOLUTE VALUE EQUATIONS

STATEMENT TRANSLATION | x | = 2: x is exactly 2 units from 0 | x | < 2: x is less than 2 units from 0 | x | > 2: x is more than 2 units from

DEFINITION |x| < a is equivalent to –a < x < a

DEFINITION |x| > a is equivalent to x a

Section 2.6 Chapter 2 Linear Equations and Inequalities

Section 2.6 Exercise #22 Chapter 2 Linear Equations and Inequalities

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Section 2.6 Exercise #23 Chapter 2 Linear Equations and Inequalities

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Section 2.6 Exercise #24 Chapter 2 Linear Equations and Inequalities

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Section 2.6 Exercise #25 Chapter 2 Linear Equations and Inequalities

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