Inequalities: Simple and Combined Relational Paths An inequality is a comparison between two numbers using the symbols "<", ">", "≤", or "≥". An equali...
An inequality is a comparison between two numbers using the symbols "<", ">", "≤", or "≥". An equality is when two numbers are equal, represented by "==".
Simple Inequalities:
Addition inequality: a > b if a is greater than b
Multiplication inequality: a < b if a is less than b
Subtraction inequality: a ≥ b if a is greater than or equal to b
These are the basic building blocks of inequalities. We can combine them to form more complex inequalities.
Combined Relational Paths:
In addition to simple inequalities, we can also combine inequalities using relational paths. These are paths that connect two inequalities together, showing how they are related.
Increasing path: if a > b and b > c, then a > c
Decreasing path: if a < b and b < c, then a > c
Examples:
5 > 3 (simple inequality)
2 + 3 > 5 (addition inequality)
4 ≤ 6 (simple inequality)
3 > 1 (increasing path)
2 < 4 (decreasing path)
By understanding these concepts, we can solve inequalities and analyze the relationships between numbers using simple and combined relational paths