Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0 and |x| = -x if x < 0. This concept is crucial for understanding how to manipulate inequalities involving absolute values.
Recommended video:
Parabolas as Conic Sections Example 1
Inequalities
Inequalities express a relationship between two expressions that are not necessarily equal. In the context of absolute value inequalities, we often deal with expressions that can be greater than or less than a certain value. Understanding how to solve and graph inequalities is essential for finding the solution set of the given absolute value inequality.
Recommended video:
Solving Absolute Value Inequalities
To solve an absolute value inequality like 3 ≤ |2x - 1|, we break it into two separate cases based on the definition of absolute value. This involves setting up two inequalities: one for the positive case (2x - 1 ≥ 3) and one for the negative case (2x - 1 ≤ -3). Solving these cases will yield the solution set for the original inequality.
Recommended video: