---
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