Solve each equation or inequality. |7x-3| > 4

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 equations and inequalities that involve it, as it leads to two possible cases based on the definition.

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal. They can be represented using symbols such as '>', '<', '≥', and '≤'. When solving inequalities, especially those involving absolute values, it is important to consider the implications of the inequality sign and how it affects the solution set, which may include multiple intervals.

Case Analysis

Case analysis is a method used to solve problems that involve conditions or multiple scenarios. In the context of absolute value inequalities, it involves breaking the problem into separate cases based on the definition of absolute value. For the inequality |7x - 3| > 4, this means solving two distinct inequalities: 7x - 3 > 4 and 7x - 3 < -4, leading to a comprehensive solution set.