In Algebra, the solution to an inequality is a range of numbers that is less than, greater than, less than or equal to, or greater than or equal to a specific value. This article introduces inequalities and demonstrates how to graph them on number lines.
Symbols for Inequalities
• Less than: <
Example: 4 < 100 (4 is less than 100.)
• Greater than: >
Example: 100 > 4 (100 is greater than 4.)
• Less than or equal to: ≤
Example: 5 ≤ 28 (5 is less than or equal to 28.)
• Greater than or equal to: ≥
Example: 28 ≥ 5 (28 is greater than or equal to 5.)
Examples of Inequalities in Algebra
- y + 5 > 12
- 195 ≤ 2x + y
- |n - 12| ≥ 0
- y < 2x2 + 4x + 2
Examples of Inequalities in the Real World
- The most money that Terrence can spend on groceries, g, is $250. (g ≤ 250)
- Amanda budgets an amount, a, of at least $100 to spend on the water bill. (a ≥ 100)
- When a child is missing for more than 48 hours, h, the local police start searching for the child. (h > 48)
- Fewer than 16 students, s, attended each review class. (s < 16)
Use the following pages to learn how to represent these inequalities on a number line.