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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.