Solve each equation or inequality. |7/2-3x| -9=0

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 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 = 0, where a and b are constants. Solving linear equations involves isolating the variable to find its value. In the context of the given problem, the absolute value equation can be transformed into two separate linear equations for solution.

Inequalities

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like <, >, ≤, or ≥. When solving inequalities, the solution set may include a range of values rather than a single point. In the context of absolute value equations, understanding how to manipulate inequalities is essential, especially when considering the implications of the absolute value definition.