In Exercises 59–94, solve each absolute value inequality. |2x - 6| < 8

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. For any real number 'a', the absolute value is denoted as |a| and is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. Understanding absolute value is crucial for solving inequalities that involve expressions within absolute value bars.

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal. They can be strict (using < or >) or non-strict (using ≤ or ≥). When solving absolute value inequalities, it is important to translate the absolute value expression into two separate inequalities that reflect the conditions under which the original inequality holds true.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). Understanding interval notation is essential for expressing the solution set of inequalities, particularly when determining the range of values that satisfy the given absolute value inequality.