Solve each equation or inequality. |8-5x| ≥ 2

Key Concepts

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 denoted as |x| and is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. Understanding absolute value is crucial for solving equations and inequalities that involve it, as it leads to two separate cases to consider.

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal, using symbols such as ≥, ≤, >, and <. When solving inequalities, it is important to maintain the direction of the inequality sign, especially when multiplying or dividing by negative numbers. This concept is essential for interpreting and solving the given absolute value inequality.

Case Analysis

Case analysis involves breaking down a problem into multiple scenarios based on different conditions. For absolute value inequalities, this means creating separate equations for the positive and negative cases of the expression inside the absolute value. This method allows for a comprehensive solution that accounts for all possible values that satisfy the original inequality.