Solve each equation. | x - 4/ 2| = 5

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the definition.

Linear Equations

Linear equations are mathematical statements that express a relationship between variables in the form of a straight line when graphed. They typically take the form ax + b = c, where a, b, and c are constants. In the context of the given equation, solving for x involves isolating the variable to find its value, which may yield multiple solutions due to the nature of absolute value.

Case Analysis

Case analysis is a problem-solving technique used to break down complex problems into simpler, manageable parts. In the context of absolute value equations, it involves considering different scenarios based on the definition of absolute value. For the equation |x - 4/2| = 5, this means setting up two separate equations: x - 4/2 = 5 and x - 4/2 = -5, allowing for a comprehensive solution.