key term - 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 quantities and express inequalities, indicating that the left-hand side is either greater than or equal to the right-hand side.

5 Must Know Facts For Your Next Test

1. The ≥ symbol is used to represent the relationship where a value on the left-hand side is greater than or equal to a value on the right-hand side.
2. When solving linear inequalities, the ≥ symbol is used to indicate that the solution set includes all values that are greater than or equal to the solution.
3. In the context of compound inequalities, the ≥ symbol is used to connect multiple simple inequalities, creating a range of values that satisfy the overall inequality.
4. Graphing linear inequalities in two variables with the ≥ symbol results in a half-plane, including the boundary line, that represents the solution set.
5. When solving rational inequalities, the ≥ symbol is used to compare the numerator and denominator expressions, leading to a solution set that satisfies the inequality.

Review Questions

• Explain how the ≥ symbol is used in the context of solving linear inequalities.
  • When solving linear inequalities, the ≥ symbol indicates that the solution set includes all values that are greater than or equal to the solution. For example, in the inequality $2x + 3 \geq 7$, the solution set would include all real numbers $x$ such that $x \geq 2$. This means the solution set is all values of $x$ that are greater than or equal to 2.
• Describe the role of the ≥ symbol in the graphing of linear inequalities in two variables.
  • When graphing linear inequalities in two variables with the ≥ symbol, the resulting graph is a half-plane that includes the boundary line. For example, the inequality $3x + 2y \geq 6$ would be graphed as a half-plane that includes the line $3x + 2y = 6$. The shaded region represents the solution set of all points $(x, y)$ that satisfy the inequality $3x + 2y \geq 6$.
• Analyze how the ≥ symbol is used in the context of solving rational inequalities.
  • In the process of solving rational inequalities, the ≥ symbol is used to compare the numerator and denominator expressions. This allows for the identification of the solution set that satisfies the overall inequality. For instance, in the inequality $\frac{x + 2}{x - 1} \geq 3$, the ≥ symbol is used to compare the rational expression on the left-hand side to the constant 3 on the right-hand side. The solution set would include all values of $x$ that make the left-hand side greater than or equal to 3.

Related terms

Inequality:

A mathematical statement that shows a relationship between two expressions where one is greater than, less than, greater than or equal to, or less than or equal to the other.

Linear Inequality:

An inequality that can be written in the form $ax + b \geq 0$, where $a$ and $b$ are constants, and $x$ is a variable.

Compound Inequality:

An inequality that combines two or more simple inequalities using the words 'and' or 'or' to create a more complex relationship between the variables.