Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Parabolas as Conic Sections Example 1
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.
Recommended video:
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.
Recommended video: