OBJECTIVES

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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Section 2.1
Linear Equations in One Variable
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DEFINITION
PROPERTIES OF EQUALITIES

For real numbers a, b, and c.

1. a a Reflexive
2. If a b, then b a Symmetric
3. If a b and b c,
   then a c Transitive

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DEFINITION
LINEAR EQUATIONS

An equation that can be written in the form
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DEFINITION
SOLUTIONS OF AN EQUATION
Replacements of the variable that make the
equation a true statement.
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DEFINITION
EQUIVALENT EQUATIONS
Two equations that have the same solution set.
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PROCEDURE
Clear fractions/decimals Remove
parentheses/simplify Add/Subtract to get variable
isolated Multiply/Divide to make coefficient 1
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DEFINITION
EQUATIONS WITH NO SOLUTIONS AND INFINITELY MANY
SOLUTIONS

No solutions(contradictions)
Infinitely many solutions(identities)
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Section 2.2
Formulas, Geometry and Problem Solving
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PROCEDURE
SOLVE FOR A SPECIFIED VALUE

1. Add or Subtract the same quantity on both sides.
2. Use the distributive property.
3. Use CRAM.

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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Section 2.3
Problem Solving Integers and Geometry
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PROCEDURE
RSTUV Method for Solving Word Problems
Read Select Think Use
Verify
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Section 2.4
Problem Solving Percent, Investment, Motion, and
Mixture Problems
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PROCEDURE
RSTUV Method for Solving Word Problems
Read Select Think Use
Verify
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Section 2.5
Linear and Compound Inequalities
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DEFINITION
LINEAR INEQUALITIES

An inequality that can be written in the form
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DEFINITION
UNION OF TWO SETS
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DEFINITION
INTERSECTION OF TWO SETS
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DEFINITION
EQUIVALENT STATEMENTS FOR AND

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OBJECTIVES
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OBJECTIVES
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Section 2.6
Absolute-Value Equations and Inequality
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DEFINITION
THE SOLUTIONS OF X A (A 0)
If a 0, the solutions of x a are x
a and x a.
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STATEMENT TRANSLATION
ABSOLUTE VALUE EQUATIONS

If expression a, where a 0 expression
a or a
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STATEMENT TRANSLATION
ABSOLUTE VALUE EQUATIONS

If expression expression, expression
expression expression (expression)
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STATEMENT TRANSLATION

x 2 x is exactly 2 units from 0 x lt 2 x
is less than 2 units from 0 x gt 2 x is more
than 2 units from 0
0
0
0
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DEFINITION
x lt a is
equivalent to a lt x lt a
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DEFINITION
x gt a is
equivalent to x lt a or x gt a
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Section 2.1
Chapter 2 Linear Equationsand Inequalities
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Section 2.1Exercise 5
Chapter 2 Linear Equationsand Inequalities
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Section 2.1Exercise 6
Chapter 2 Linear Equationsand Inequalities
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Section 2.2
Chapter 2 Linear Equationsand Inequalities
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Section 2.2Exercise 7
Chapter 2 Linear Equationsand Inequalities
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a. Solve for h.
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a. Solve for h.
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Section 2.2Exercise 9
Chapter 2 Linear Equationsand Inequalities
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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?
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a. Solve for L.
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b. If the perimeter is 100 ft and the length
is 20 ft more than the width, what are the
dimensions of the rectangle?
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b. If the perimeter is 100 ft and the length
is 20 ft more than the width, what are the
dimensions of the rectangle?
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Section 2.2Exercise 10
Chapter 2 Linear Equationsand Inequalities
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These are the alternate exterior anglesand they
are equal.
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Section 2.3
Chapter 2 Linear Equationsand Inequalities
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Section 2.3Exercise 11
Chapter 2 Linear Equationsand Inequalities
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The bill for repairing an appliance totaled
72.50. If the repair shop charges 35 for the
service call, plus25 for each hour of labor,
how many hourslabor did the repair take?
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Section 2.4
Chapter 2 Linear Equationsand Inequalities
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Section 2.4Exercise 14
Chapter 2 Linear Equationsand Inequalities
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An investor bought some municipal bonds yielding
5 percent annually and some certificates of
deposit yielding 7 percent. If his total
investmentamounts to 20,000 and his annual
interestis 1100, how much money is invested
inbonds and how much in certificates ofdeposit?
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Section 2.4Exercise 15
Chapter 2 Linear Equationsand Inequalities
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A freight train leaves a station traveling at 40
mi/hr.Two hours later, a passenger train leaves
thesame station traveling in the same
directionat 60 mi/hr. How far from the station
does thepassenger train overtake the freight
train?
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Their distances are equal
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Their distances are equal
The passenger train overtakes thefreight train
240 miles from the station.
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Section 2.5
Chapter 2 Linear Equationsand Inequalities
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Section 2.5Exercise 18
Chapter 2 Linear Equationsand Inequalities
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Section 2.5Exercise 19
Chapter 2 Linear Equationsand Inequalities
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Section 2.5Exercise 20
Chapter 2 Linear Equationsand Inequalities
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and
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Section 2.5Exercise 21
Chapter 2 Linear Equationsand Inequalities
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Section 2.6
Chapter 2 Linear Equationsand Inequalities
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Section 2.6Exercise 22
Chapter 2 Linear Equationsand Inequalities
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or
or
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Section 2.6Exercise 23
Chapter 2 Linear Equationsand Inequalities
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Section 2.6Exercise 24
Chapter 2 Linear Equationsand Inequalities
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Section 2.6Exercise 25
Chapter 2 Linear Equationsand Inequalities
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