In Exercises 51–58, solve each compound inequality. - 3 ≤ x - 2 < 1

Key Concepts

Compound Inequalities

A compound inequality consists of two or more inequalities that are combined into one statement by the words 'and' or 'or'. In this case, the compound inequality '3 ≤ x - 2 < 1' indicates that x must satisfy both conditions simultaneously. Understanding how to interpret and solve these inequalities is crucial for finding the values of x that meet the criteria.

Solving Inequalities

Solving inequalities involves isolating the variable on one side of the inequality sign. This process is similar to solving equations but requires special attention to the direction of the inequality sign, especially when multiplying or dividing by negative numbers. Mastery of this technique is essential for accurately determining the solution set for compound inequalities.

Interval Notation

Interval notation is a way of expressing the solution set of inequalities using intervals. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, the solution to the compound inequality can be expressed in interval notation, which provides a clear and concise way to represent the range of values that satisfy the inequality.