Chapter 9: Exploring Inequalities
Inequalities are mathematical statements that compare two
values or expressions, indicating that one is larger or smaller
than the other. This chapter introduces the concept of
inequalities, how to solve them, and their graphical
representation, expanding the understanding of algebraic
relationships.
Introduction to Inequalities and Their Notation
Inequalities express the relationship between two quantities
that are not equal. The primary symbols used in inequalities
are: -
- \( > \) (greater than)
- \( < \) (less than)
- \( \geq \) (greater than or equal to)
- \( \leq \) (less than or equal to)
For example, \( x > 3 \) means that \( x \) is any number greater
than 3. Unlike equations, where each side must be equal,
inequalities show a range of possible values for the variables
involved.
Solving Simple Inequalities
Solving inequalities involves finding all possible values of the
variable that make the inequality true. The process is similar to
solving equations, with the added rule that if you multiply or
divide by a negative number, you must reverse the inequality
sign.
For instance, to solve \( -2x < 6 \), we divide both sides by -2,
which reverses the inequality sign, resulting in \( x > -3 \).
Inequalities are mathematical statements that compare two
values or expressions, indicating that one is larger or smaller
than the other. This chapter introduces the concept of
inequalities, how to solve them, and their graphical
representation, expanding the understanding of algebraic
relationships.
Introduction to Inequalities and Their Notation
Inequalities express the relationship between two quantities
that are not equal. The primary symbols used in inequalities
are: -
- \( > \) (greater than)
- \( < \) (less than)
- \( \geq \) (greater than or equal to)
- \( \leq \) (less than or equal to)
For example, \( x > 3 \) means that \( x \) is any number greater
than 3. Unlike equations, where each side must be equal,
inequalities show a range of possible values for the variables
involved.
Solving Simple Inequalities
Solving inequalities involves finding all possible values of the
variable that make the inequality true. The process is similar to
solving equations, with the added rule that if you multiply or
divide by a negative number, you must reverse the inequality
sign.
For instance, to solve \( -2x < 6 \), we divide both sides by -2,
which reverses the inequality sign, resulting in \( x > -3 \).
