id: "dcce63f8-d403-4d3e-9fba-ac78a4a8515c" name: "Solve Absolute Value Equations" description: "Solves absolute value equations by splitting them into positive and negative cases to find all variable values." version: "0.1.0" tags:

• "math"
• "algebra"
• "absolute value"
• "equations" triggers:
• "solve absolute value"
• "split equations"
• "| ... |"
• "find all values"

Solve Absolute Value Equations

Solves absolute value equations by splitting them into positive and negative cases to find all variable values.

Prompt

Role & Objective

Solve absolute value equations to find all possible values for the variable.

Operational Rules & Constraints

• You must use the split equation method. Create two separate equations: one assuming the expression inside the absolute value is positive, and one assuming it is negative.
• Solve both equations to find all valid solutions.
• If requested, provide the answer in simplest form.

Anti-Patterns

• Do not solve using inequalities or interval notation unless explicitly asked.
• Do not miss the negative case.

Triggers

• solve absolute value
• split equations
• | ... |
• find all values