54
L7
§2.1 Linear Equations
Types of Equations
Identity
:
An equation satisfied by every number that is
a meaningful replacement for the variable.
Example
:
32
125
(
5)(
5
25)
xx
x
x
−=
−
+
+
.
Conditional equations
: Equations satisfied by some
numbers but not by others.
Example
: 2(
5)
3
x
x
+=
.
Contradiction
:
An equation that is false for every
value of the variable.
Example
: 3(
3)
3
3
x
x
+
.
Such an equation has solution set
∅
(empty).
This happens whenever you solve and get a ridiculous
statement (see the example above).
Definition
. Equations with the same solution set are
called
equivalent equations
.
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Linear Equations
Definition
. An equation of the form
0
ax
b
+
=
,
where
0
a
≠
, is called a
linear equation.
Solving Linear Equations
:
Simplify both sides as much as possible. Get terms
with variable on one side and numbers on the other.
Simplify and solve for the variable.
Example
.
Solve:
3(3 2 )
33 2
x
x
−
=−
Solving equations involving rational expressions
:
1. Multiply each term in the equation by the LCD of all
fractions and write down restrictions on the variable.
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 Fall '11
 gregory
 Linear Equations, Equations, Quadratic equation, Complex number, Example. Solve

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