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Tutorial - How to Graph Inequalities

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Tutorial - How to Graph Inequalities

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.

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