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Real numbers include all the numbers you could possibly need in everyday mathematics. They can be made up of fractions, decimals, integers, whole numbers, and even irrational numbers like pi and square roots.
- **Integers** are positive and negative whole numbers, including zero, that do not have any decimal or fractional parts. - **Fractions and Decimals** can represent numbers between whole numbers, allowing for precise calculations involving not whole unit quantities.
Even numbers such as -15 and its counterparts on the positive side of the number line are real numbers. In our inequality problem, we are focusing on all real numbers, which means considering the entire set of numbers that can be placed on an infinite numerical line extending in both directions.

An inequality sign represents a relationship between two values, showing that one value is either greater than or less than another. In mathematics, when you want to express that one value is smaller than another, you use the sign '<'.
For example, in our exercise, to express that a group of numbers are less than -15, we utilize this sign. Thus, the statement is denoted as:
\[x < -15\]This simple sign plays a crucial role in mathematical expressions and communicates the relationship between values, clarifying how a variable behaves in terms of size relative to another number. It's an essential tool in algebra that helps in forming conditions and constraints.

Algebraic expressions are combinations of numbers and variables connected through arithmetic operations like addition, subtraction, multiplication, and division. These expressions help translate words or concepts into mathematical language.
To write an inequality involving real numbers, we often choose a variable like \( x \) to represent an unknown quantity or a set of quantities. In our exercise, \( x \) symbolizes any real number that is less than -15.
The expression \( x < -15 \) is an example of an algebraic inequality. It converts a verbal description "all real numbers less than -15" into a succinct mathematical form. This transformation is vital because it lets us handle practical problems concerning wide ranges of possible values using mathematical methods. By understanding and employing algebraic expressions, students develop a critical component of their mathematical toolkit.