Greater Than or Equal To (≥)

Definition

The symbol '≥' is a mathematical operator that represents the relationship where one value is greater than or equal to another value. It is used to compare two quantities and indicates that the value on the left side is greater than or equal to the value on the right side.

5 Must Know Facts For Your Next Test

1. The '≥' symbol is used to represent the 'greater than or equal to' relationship between two values in a mathematical expression.
2. When solving systems of nonlinear equations and inequalities, the '≥' symbol is used to define the boundaries of the solution set.
3. Inequalities with the '≥' symbol can be graphed on the coordinate plane, and the solution set is represented by the region on one side of the boundary line.
4. The '≥' symbol is often used in optimization problems to represent constraints, such as resource limitations or minimum requirements.
5. Understanding the properties and behavior of the '≥' symbol is crucial for correctly solving systems of nonlinear equations and inequalities involving two variables.

Review Questions

• Explain how the '≥' symbol is used in the context of systems of nonlinear equations and inequalities with two variables.
  • In the context of systems of nonlinear equations and inequalities with two variables, the '≥' symbol is used to define the boundaries of the solution set. The inequality with the '≥' symbol represents a region on the coordinate plane where the solution must lie. When solving these systems, the '≥' inequality is used to describe the constraints or limitations on the variables, and the solution set is the intersection of the regions defined by the various inequalities in the system.
• Describe the graphical representation of an inequality with the '≥' symbol in a system of nonlinear equations and inequalities with two variables.
  • When graphing an inequality with the '≥' symbol in a system of nonlinear equations and inequalities with two variables, the boundary line is drawn as a solid line. The solution set is the region on the coordinate plane that is on one side of the boundary line, including the boundary line itself. This means that the points on the boundary line and the points in the region satisfying the inequality are all considered part of the solution set.
• Analyze the role of the '≥' symbol in optimization problems involving systems of nonlinear equations and inequalities with two variables.
  • In optimization problems involving systems of nonlinear equations and inequalities with two variables, the '≥' symbol is often used to represent constraints or minimum requirements. For example, an inequality with the '≥' symbol may be used to describe a resource limitation or a minimum production target that must be met. The '≥' symbol ensures that the solution satisfies these constraints, and the optimal solution is the point within the feasible region that maximizes or minimizes the objective function.

Related terms

Inequality: A mathematical statement that compares two expressions using an inequality symbol such as >, <, ≥, or ≤.

System of Inequalities: A set of two or more inequalities that must be satisfied simultaneously.

Nonlinear Equations: Equations that contain variables raised to a power other than 1, or variables multiplied or divided by each other.