MATH10-1
COLLEGE ALGEBRA
LINEAR EQUATIONS IN ONE
VARIABLE AND APPLICATIONS

GENERAL OBJECTIVE
•
Classify equations as linear, fractional, or rational,
•
Solve linear equations,
•
Solve equations leading to the form
ax
+
b
= 0,
and
•
Solve application problems involving linear equations by
developing mathematical models for real-life problems.
At the end of the lesson the students are expected to:

TODAY’S OBJECTIVE
•
Identify an equation,
•
Classify equations as identity, conditional or equivalent,
•
Distinguish a consistent from an inconsistent equation,
•
Enumerate the properties of equality.
At the end of the lesson the students are expected to:

DEFINITION
EQUATION

KINDS OF EQUATIONS
2

•
Two equations with exactly the same solutions are called
equivalent equations.
Example:
The following are equivalent equations.
4
.
c
22
2
5
.
b
20
5
.
a
x
x
x

EXAMPLEDetermine whether the given equation is an identity or aconditional equation.
15

For all real numbers
a
,
b
, and
c
1
.
Addition Property of Equality
If
a = b
then
a + c = b + c
2
.
Subtraction Property of Equality
If
a = b
then
a – c = b – c
3
.
Multiplication Property of Equality
If
a = b
then
a
c =
b
c
∙
∙
4
.
Division Property of Equality
If
a = b
then
PROPERTIES OF EQUALITY
0
where
c
c
b
c
a

TODAY’S OBJECTIVE
•
Define linear equations in one variable,
•
Determine the difference between linear and nonlinear
equations,
•
Enumerate the steps in solving linear equations,
•
Solve linear equations and equations involving fractions,
•
Solve rational equations which are reducible to linear
equations,
•
Define extraneous solution.
At the end of the lesson the students are expected to:

RECALL
•
An
identity
equation
is an equation that is true for any number
substituted to the variable.
•
An
equation
is a statement that two mathematical expressions
are equivalent or equal.
•
A
conditional equation
is an equation that is true only for certain
values of the unknown.
•
Two equations with exactly the same solutions are called
equivalent equations.
•
An
inconsistent equation
is an equation that has no solution.
•
A
consistent equation
is an equation that has a solution.

DEFINITION

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- Spring '12
- edgar
- Math, Algebra, Linear Equations, Equations, Quadratic equation, Quintic equation, Redlin