Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Inequalities And Absolute Values
Introduction: Different Ways to Say the Same Thing
Mathematicians have developed several languages to describe the solution sets of inequalities. Just as you can say "hello," "hi," or "greetings," you can express the solution x is greater than 5 in multiple ways: as an inequality (x > 5), as a sentence in set notation, or as an interval on a number line.
Understanding these different notations is essential for communicating mathematical ideas clearly and for interpreting answers you might see in textbooks or on standardized tests. This lesson will explore compound inequalities, set notation, and interval notation.
Compound Inequalities
A compound inequality is a statement that combines two or more inequalities. There are two main types:
- "And" Inequalities (Intersection)
Both conditions must be true at the same time. Often written as a single statement like x > 5 and x < 10, or more compactly as 5 < x < 10. The solution is the intersection of the two conditions—the numbers that satisfy both. On a graph, this appears as a single connected interval between two points.
- Both conditions must be true at the same time.
- Often written as a single statement like x > 5 and x < 10, or more compactly as 5 < x < 10.
- The solution is the intersection of the two conditions—the numbers that satisfy both.
- On a graph, this appears as a single connected interval between two points.
- "Or" Inequalities (Union)