CHAPTER 2
Equations and Inequalities
Source:
Elementary & Intermediate Algebra, Fourth Edition
Prepared and Edited by:
Dr. Mohamad Hammoudi

Topics of Chapter 2
2.1: Solving Equations by Adding and Subtracting.
2.2: Solving Equations by Multiplying and Dividing.
2.3:Combining the Rules to Solve Equations.
2.8:
Solving Inequalities Using Addition.
2.9: Solving Inequalities Using Multiplication.
2

2.1: Solving Equations by Adding and Subtracting
Objectives:
2.1.1: Determine whether a given number is a
solution for an equation
2.1.2: Use the addition property to solve equations
2.1.3: Determine whether a given number is a
solution for an application
2.1.4: Translate words to equation symbols
2.1.5: Solve application problems
3

Equation
Definition of Equation
An
equation
is a mathematical statement that two
expressions
are
equal
.
Some examples are 3 + 4 = 7,
x + 3 = 5, P = 2L + 2W.
As you can see, an equal sign (=) separates the two equal
expressions.
These expressions are usually called the
left side
and the
right side
of the equation.
4

Equation
An equation may be either true or false.
Any number can replace x for the following equation
x + 3 = 5
The number 2 is called the
solution
(or root) of the equation
x + 3 = 5 because
substituting 2 for
x gives a
true
statement. The
set {2}
is called the
solution set
.
5

Solution and Solution Set
Definition of Solution
A
solution
for an equation is any value for the variable that
makes the equation a
true
statement.
Definition of Solution Set
The
solution set
for an equation is the set of
all values
for
the variables that make the equation a
true
statement
.
Some equations may have more than one solution.
Example: x
2
= 9
Solution (3)
2
= 9 and (
–
3)
2
= 9
Solution Set = {3,
–
3}
6

2.1.1: Determine whether a given number is a solution for
an equation
Examples:
1.
Is 3 a solution for the equation 2
x +
4 = 10?
2.
Is
a solution of the equation 3
x
–
= 2
x +
1?
3
5
3
2
7

Degree of Equation
The
degree of an
equation in one variable is the highest
power to which the variable is raised.
5
x
4
–
9
x
2
+ 7
x
–
2 = 0
The highest power to which the
x is raised is
four
.
Therefore, it is called a
fourth
-degree equation.
x
+ 3 = 5
The highest power to which the
x is raised is
one
.
Therefore, it is called a
first
-degree equation or
linear
equation
. This chapter will discuss
linear equations.
x
2
–
3 = 6. This is a
second
-degree equation and is called
quadratic equation
.

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