Solving Absolute Value Equations: Isolating the Absolute Value

Isolating Absolute Value Expressions

• The primary and foundational step when solving absolute value equations or inequalities is to isolate the absolute value expression on one side of the equal sign or inequality symbol.
• Procedure for scalar isolation:
  • Identify any operations acting upon the absolute value expression, such as division by a constant denominator.
  • Multiply both sides of the equation by $4$ to clear the fraction/division and completely isolate the absolute value term.
  • Once the absolute value term is isolated on one side, proceed to set up and solve the resulting algebraic equations for both the positive and negative cases.