Solve each equation. |7 - 3x| = 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 '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 that involve it, as it leads to two possible cases based on the definition.

Linear Equations

A linear equation is an equation of the first degree, meaning it involves only linear terms and can be expressed in the form ax + b = c, where a, b, and c are constants. Solving linear equations often involves isolating the variable on one side of the equation. In the context of absolute value equations, each case derived from the absolute value will lead to a linear equation that can be solved for the variable.

Case Analysis

Case analysis is a method used to solve equations that can yield multiple solutions based on different scenarios. For absolute value equations, this involves setting up separate equations for each case derived from the absolute value definition. In the example |7 - 3x| = 3, we create two cases: 7 - 3x = 3 and 7 - 3x = -3, allowing us to find all possible solutions for x.