Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x<-6

Verified step by step guidance

1. Identify the inequality given: \( x < -6 \).
2. Understand that \( x < -6 \) means all values of \( x \) are less than \(-6\).
3. In interval notation, this is represented as \((-\infty, -6)\).
4. The parenthesis \((-\infty, -6)\) indicates that \(-6\) is not included in the interval, and the interval extends to negative infinity.
5. Match the inequality \( x < -6 \) with its equivalent interval notation \((-\infty, -6)\) in Column II.

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Understanding how to interpret and manipulate inequalities is essential for solving problems that involve ranges of values.

Interval Notation

Interval notation is a way of representing a set of numbers between two endpoints. It uses parentheses and brackets to indicate whether the endpoints are included (closed interval) or excluded (open interval). For example, the interval (-∞, -6) represents all numbers less than -6, which corresponds to the inequality x < -6.

Graphing Inequalities

Graphing inequalities involves representing the solutions of an inequality on a number line. For the inequality x < -6, the graph would show an open circle at -6 (indicating that -6 is not included) and a shaded line extending to the left, representing all values less than -6. This visual representation helps in understanding the range of solutions that satisfy the inequality.