Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2

Verified step by step guidance

1. Identify the inequality given: \(-2 < x \leq 6\).
2. Understand that \(-2 < x\) means \(x\) is greater than \(-2\) but not equal to \(-2\).
3. Understand that \(x \leq 6\) means \(x\) is less than or equal to \(6\).
4. Combine these two parts to describe the range of \(x\): \(x\) is between \(-2\) and \(6\), not including \(-2\) but including \(6\).
5. Translate this range into interval notation: \((-2, 6]\).

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 <, >, ≤, and ≥. 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 (-2, 6] includes all numbers greater than -2 and up to and including 6.

Graphing Inequalities

Graphing inequalities involves representing the solution set of an inequality on a number line. This visual representation helps in understanding the range of values that satisfy the inequality. For the inequality -2 < x ≤ 6, the graph would show an open circle at -2 and a closed circle at 6, indicating the values that x can take.