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: \( x \geq -6 \).
2. Understand that \( x \geq -6 \) means \( x \) is greater than or equal to \(-6\).
3. Recall that in interval notation, a square bracket \([\) or \(]\) indicates that the endpoint is included in the interval.
4. Since \( x \) can be equal to \(-6\), use a square bracket at \(-6\).
5. The interval notation for \( x \geq -6 \) is \([-6, \infty)\), where \(\infty\) always uses a parenthesis because infinity is not a number that can be reached.

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 '≥' (greater than or equal to), '≤' (less than or equal to), '>' (greater than), and '<' (less than). Understanding how to interpret and manipulate inequalities is essential for solving problems that involve ranges of values.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded. For example, the interval notation for 'x ≥ -6' is written as '[-6, ∞)', indicating that -6 is included in the interval, while the upper limit extends indefinitely.

Graphing Inequalities

Graphing inequalities involves representing the solutions of an inequality on a number line. For 'x ≥ -6', the graph would include a solid dot at -6 (indicating that -6 is part of the solution) and a line extending to the right, showing all values greater than -6. This visual representation helps in understanding the range of solutions and their relationships.