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Definition

The symbol '>' represents a greater than relation in mathematics, indicating that one value is larger than another. This concept is fundamental when dealing with inequalities, allowing us to express and analyze relationships between numbers or expressions. Understanding this symbol is essential for solving linear inequalities and systems of inequalities, as well as for evaluating fairness in voting methods where comparisons are necessary.

5 Must Know Facts For Your Next Test

1. '>' is used in inequalities to indicate that the number on the left side is larger than the number on the right side.
2. When solving linear inequalities, reversing the direction of '>' occurs when both sides are multiplied or divided by a negative number.
3. In a system of linear inequalities, the '>' symbol helps determine which side of a boundary line should be shaded to represent all solutions.
4. In voting methods, a candidate can be deemed more favorable if their score is greater than that of another candidate based on certain criteria.
5. The interpretation of '>' in graphical representations allows for visual understanding of solutions to inequalities and comparative outcomes.

Review Questions

• How does the '>' symbol change when dealing with negative numbers during inequality manipulations?
  • '>' indicates that the left value is greater than the right value. However, when both sides of an inequality are multiplied or divided by a negative number, this relationship reverses; for instance, if you have -2 > -5 and you multiply both sides by -1, it becomes 2 < 5. Understanding this reversal is crucial when solving inequalities correctly.
• Discuss how the concept of 'greater than' applies to graphing systems of linear inequalities.
  • '>' is used to define the area of solutions above a boundary line when graphing linear inequalities. For example, if we have y > 2x + 3, the boundary line would be y = 2x + 3, and we would shade the region above this line to indicate all points (x,y) that satisfy the inequality. The visual representation helps in easily identifying feasible solutions for given constraints.
• Evaluate how the 'greater than' relationship impacts fairness in voting methods and outcomes.
  • The 'greater than' relationship is crucial in evaluating fairness in voting methods by comparing candidates' scores or preferences. For example, if Candidate A receives more votes than Candidate B, we can express this relationship as A's score > B's score. This comparison helps analyze whether voting methods accurately reflect voter preferences and can highlight potential biases or inequities in the election process.

Related terms

Inequality: A mathematical statement that compares two values or expressions, indicating that one is greater than, less than, or not equal to the other.

Boundary Line: In graphing systems of inequalities, it is the line representing the equation of the inequality, which helps to define the regions where the inequality holds true.

Voting Power: The effectiveness of a voter in influencing the outcome of an election, often analyzed using methods that incorporate the concept of greater than in determining fairness.