key term - <

Definition

The less than symbol, <, is a mathematical symbol used to represent the relationship of one value being smaller or less than another value. It is a fundamental concept in mathematics and algebra, with applications across various topics such as decimals, linear inequalities, and graphing.

5 Must Know Facts For Your Next Test

1. The less than symbol, <, is used to indicate that one value is smaller or less than another value.
2. In the context of decimals, the < symbol is used to compare the relative size of decimal numbers, such as determining if one decimal is less than another.
3. When solving linear inequalities, the < symbol is used to represent the inequality, and the solution set includes all values that make the inequality true.
4. Graphing linear inequalities on a coordinate plane involves shading the region where the inequality is true, with the < symbol indicating that the shaded region is on the left side of the boundary line.
5. In systems of linear inequalities, the < symbol is used to represent multiple inequalities that must be satisfied simultaneously, with the solution set being the intersection of the individual inequality solutions.

Review Questions

• Explain how the < symbol is used in the context of decimals.
  • In the context of decimals, the < symbol is used to compare the relative size of decimal numbers. For example, the statement $3.14 < 3.15$ indicates that the decimal value 3.14 is less than the decimal value 3.15. This allows for the ordering and comparison of decimal numbers, which is essential for understanding and working with decimals in various mathematical operations and applications.
• Describe how the < symbol is used when solving linear inequalities.
  • When solving linear inequalities, the < symbol is used to represent the inequality. For example, the inequality $2x + 3 < 5$ indicates that the value of the expression $2x + 3$ must be less than 5 for the inequality to be true. The solution set for this inequality includes all values of $x$ that make the inequality true, which can be represented on a number line or graph.
• Analyze the role of the < symbol in the context of graphing systems of linear inequalities.
  • When graphing systems of linear inequalities, the < symbol is used to represent multiple inequalities that must be satisfied simultaneously. The solution set for the system is the intersection of the individual inequality solutions, which is the region where all the inequalities are true. The < symbol, along with other inequality symbols, helps determine the boundaries and shaded regions on the graph, allowing for the visualization and interpretation of the solutions to the system of linear inequalities.

Related terms

Inequality: A mathematical statement that compares two values using symbols like <, >, ≤, or ≥ to indicate the relationship between them.

Linear Inequality:

An inequality that can be expressed in the form $ax + b < cx + d$, where $a$, $b$, $c$, and $d$ are constants and $x$ is a variable.

Graphing:

The process of representing mathematical relationships, such as inequalities, on a coordinate plane or graph.