Solve each inequality. Give the solution set in interval notation. See Example 4. -5<5+2x<11

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). Solving inequalities involves finding the range of values that satisfy the given condition.

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 in the set. For example, (a, b) means all numbers between a and b, excluding a and b, while [a, b] includes both endpoints. This notation is essential for clearly expressing the solution set of inequalities.

Compound Inequalities

Compound inequalities involve two or more inequalities that are combined into one statement, often using the word 'and' or 'or'. In the given question, -5 < 5 + 2x < 11 is a compound inequality that requires solving for x in a way that satisfies both conditions simultaneously. Understanding how to manipulate and solve these inequalities is crucial for finding the correct solution set.