key term - >

Definition

The greater than symbol (>) is a mathematical operator used to indicate that one value is greater than another. It is a fundamental concept in algebra and is used extensively in various topics, including decimals, linear inequalities, applications with linear inequalities, graphs of linear inequalities, and graphing systems of linear inequalities.

5 Must Know Facts For Your Next Test

1. The greater than symbol (>) is used to indicate that a value on the left side of the symbol is larger than the value on the right side.
2. In the context of decimals, the greater than symbol is used to compare the size of decimal numbers, such as $3.14 > 2.78$.
3. When solving linear inequalities, the greater than symbol is used to represent the relationship between the variable and the constant, such as $x > 5$.
4. In applications with linear inequalities, the greater than symbol is used to model real-world situations where one quantity must be greater than another, such as the number of hours worked being greater than 40.
5. The graph of a linear inequality with the greater than symbol is a half-plane above the corresponding line.

Review Questions

• Explain how the greater than symbol (>) is used in the context of decimals.
  • In the context of decimals, the greater than symbol (>) is used to compare the size of decimal numbers. For example, the expression $3.14 > 2.78$ indicates that the decimal number 3.14 is larger than the decimal number 2.78. This comparison of decimal values is essential for understanding the relative magnitude of numbers and is a fundamental skill in working with decimals.
• Describe how the greater than symbol (>) is used in solving linear inequalities.
  • When solving linear inequalities, the greater than symbol (>) is used to represent the relationship between the variable and the constant. For instance, the inequality $x > 5$ indicates that the variable $x$ must be a value that is greater than 5. This type of inequality is crucial in modeling real-world situations where one quantity must be greater than another, such as the number of hours worked being greater than 40 or the amount of money in a bank account being greater than a certain threshold.
• Analyze the role of the greater than symbol (>) in the graphs of linear inequalities.
  • The graph of a linear inequality with the greater than symbol (>) is a half-plane above the corresponding line. This means that the solution set for the inequality $x > 5$ would be the set of all points on the coordinate plane that are above the horizontal line $y = 5$. Understanding the graphical representation of linear inequalities with the greater than symbol is essential for visualizing and interpreting the solutions to these types of algebraic expressions.

Related terms

Less Than:

The opposite of greater than, the less than symbol (<) indicates that one value is smaller than another.

Inequality: A mathematical statement that shows a relationship between two expressions, where one is greater than, less than, or not equal to the other.

Linear Inequality:

An inequality that can be written in the form $ax + b > 0$, where $a$ and $b$ are constants, and $x$ is a variable.