Greater Than or Equal To (≥)

Definition

The symbol '≥' is a mathematical operator that represents the relationship of being greater than or equal to a specific value. It is used to compare two quantities and indicate that one is greater than or equal to the other.

5 Must Know Facts For Your Next Test

1. The symbol '≥' is used to represent the relationship of being greater than or equal to a specific value.
2. Linear inequalities with the '≥' symbol are solved by using the same methods as solving linear equations, but the solution set is a range of values rather than a single point.
3. Graphs of linear inequalities with the '≥' symbol are represented by shading the half-plane that includes the points satisfying the inequality.
4. When solving systems of linear inequalities, the '≥' symbol is used to describe the boundaries of the feasible region, which is the area where all the inequalities are satisfied simultaneously.
5. The '≥' symbol is commonly used in real-world applications, such as in setting minimum requirements or constraints, to ensure that a specific condition is met or exceeded.

Review Questions

• How do you solve a linear inequality with the '≥' symbol?
  • To solve a linear inequality with the '≥' symbol, you follow the same steps as solving a linear equation, but the solution set will be a range of values rather than a single point. This involves isolating the variable on one side of the inequality, performing the same operations on both sides, and determining the set of values that satisfy the inequality. The final solution is represented by a range of values, which can be expressed using set notation or by graphing the inequality on a number line.
• Explain the process of graphing a linear inequality with the '≥' symbol.
  • When graphing a linear inequality with the '≥' symbol, the goal is to represent the set of points that satisfy the inequality on a coordinate plane. To do this, you first graph the corresponding linear equation by drawing a solid line. Then, you determine the direction of the inequality (whether the solution set is above or below the line) and shade the appropriate half-plane. The shaded region represents the set of points that satisfy the inequality. The boundary line is included in the solution set, as indicated by the use of the '≥' symbol.
• Describe how the '≥' symbol is used in the context of solving systems of linear inequalities.
  • $$\text{When solving systems of linear inequalities, the '≥' symbol is used to describe the boundaries of the feasible region, which is the area where all the inequalities are satisfied simultaneously. The feasible region is the intersection of the half-planes defined by the individual inequalities. To find the feasible region, you graph each inequality with the '≥' symbol, and the area where all the shaded regions overlap represents the solutions that satisfy the entire system of linear inequalities.}$$

Related terms

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

Linear Inequality: An inequality in which the variable is raised to the first power, forming a linear equation.

Graphing Inequalities: The process of representing an inequality on a coordinate plane, typically by shading the region that satisfies the inequality.