Writing and Graphing Inequalities
This page introduces the concept of inequalities and how they differ from expressions and equations. It explains how to graph inequalities on a number line and interpret their solutions.
Definition: An inequality is a mathematical statement that compares two expressions using inequality symbols <,>,≤,≥.
The page illustrates the differences between expressions, equations, and inequalities:
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Expression e.g.,5x+2: This is a combination of numbers and variables without an equal sign.
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Equation e.g.,5x+2=12orx=3: These have a single, specific solution.
Example: In the equation x=3, x can only be 3.
- Inequality e.g.,x≤−2orx>3: These have multiple solutions.
Example: In the inequality x>3, x can be 3 or any number greater than 3.
The page also explains how to graph inequalities on a number line:
- For inequalities including the equal sign ≤or≥, use a closed dot on the number line.
- For strict inequalities <or>, use an open dot on the number line.
Highlight: When graphing x≤-2, use a closed dot at -2 because -2 is included in the solution set.
Vocabulary:
- Closed Dot: Used when the endpoint is included in the solution set ≤or≥.
- Open Dot: Used when the endpoint is not included in the solution set <or>.
This introduction to writing and graphing inequalities provides a foundation for more advanced topics in algebra and helps students visualize the solution sets of inequalities.