Inequalities are used to demonstrate relationships between numbers or expressions.
LEARNING OBJECTIVES
Explain what inequalities represent and how they are used
KEY TAKEAWAYS
Key Points
An inequality describes a relationship between two different values.
The notation
a
<
b
means that
a
is strictly smaller in size than
b
, while the notation
a
>
b
means that
a
is strictly greater than
b
.
The notion
a
≤
b
means that
a
is less than or equal to
b
, while the notation
a
≥
b
means that
a
is greater than or equal to
b
.
Inequalities are particularly useful for solving problems involving minimum or maximum possible values.
Key Terms
number line: A visual representation of the set of real numbers as a series of points.
inequality: A statement that of two quantities one is specifically less than or greater than another.
In mathematics, inequalities are used to compare the relative size of values. They can be used to compare integers, variables, and various other algebraic expressions. A description of different types of inequalities follows.
Strict Inequalities
A strict inequality is a relation that holds between two values when they are different. In the same way that equations use an equals sign, =, to show that two values are equal, inequalities use signs to show that two values are not equal and to describe their relationship. The strict inequality symbols are
<
and
>
.
Strict inequalities differ from the notation
a
≠
b
, which means that a is not equal to
b
. The
≠
symbol does not say that one value is greater than the other or even that they can be compared in size.
In the two types of strict inequalities,
a
is not equal to
b
. To compare the size of the values, there are two types of relations:
The notation
a
<
b
means that
a
is less than
b
.
The notation
a
>
b
means that
a
is greater than
b
.
The meaning of these symbols can be easily remembered by noting that the “bigger” side of the inequality symbol (the open side) faces the larger number. The “smaller” side of the symbol (the point) faces the smaller number.
Answers & Comments
Introduction to Inequalities
Inequalities are used to demonstrate relationships between numbers or expressions.
LEARNING OBJECTIVES
Explain what inequalities represent and how they are used
KEY TAKEAWAYS
Key Points
An inequality describes a relationship between two different values.
The notation
a
<
b
means that
a
is strictly smaller in size than
b
, while the notation
a
>
b
means that
a
is strictly greater than
b
.
The notion
a
≤
b
means that
a
is less than or equal to
b
, while the notation
a
≥
b
means that
a
is greater than or equal to
b
.
Inequalities are particularly useful for solving problems involving minimum or maximum possible values.
Key Terms
number line: A visual representation of the set of real numbers as a series of points.
inequality: A statement that of two quantities one is specifically less than or greater than another.
In mathematics, inequalities are used to compare the relative size of values. They can be used to compare integers, variables, and various other algebraic expressions. A description of different types of inequalities follows.
Strict Inequalities
A strict inequality is a relation that holds between two values when they are different. In the same way that equations use an equals sign, =, to show that two values are equal, inequalities use signs to show that two values are not equal and to describe their relationship. The strict inequality symbols are
<
and
>
.
Strict inequalities differ from the notation
a
≠
b
, which means that a is not equal to
b
. The
≠
symbol does not say that one value is greater than the other or even that they can be compared in size.
In the two types of strict inequalities,
a
is not equal to
b
. To compare the size of the values, there are two types of relations:
The notation
a
<
b
means that
a
is less than
b
.
The notation
a
>
b
means that
a
is greater than
b
.
The meaning of these symbols can be easily remembered by noting that the “bigger” side of the inequality symbol (the open side) faces the larger number. The “smaller” side of the symbol (the point) faces the smaller number.