Solve each equation or inequality. | 5x + 2 | - 2 < 3

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 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 can lead to two separate cases to consider.

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal, using symbols such as <, >, ≤, or ≥. When solving inequalities, it is important to maintain the direction of the inequality when performing operations, especially when multiplying or dividing by a negative number. This concept is essential for determining the solution set of the given inequality.

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 |5x + 2| - 2 < 3, we will consider two cases: when the expression inside the absolute value is non-negative and when it is negative, leading to different equations to solve.