Absolute Value Equation / Inequality Calculator
Solves absolute value equations and inequalities.
Info
This tool solves basic absolute value equations and first-degree inequalities. General form: - Equation: |a·x + b| = c - Inequality: |a·x + b| ≤ c, |a·x + b| < c, |a·x + b| ≥ c, |a·x + b| > c Basic rules: - In |t| = c, there is no solution if c < 0 (empty set). - For |t| = c with c ≥ 0, two equations are written: t = c or t = -c. - For |t| ≤ c: -c ≤ t ≤ c (closed interval) - For |t| < c: -c < t < c (open interval) - For |t| ≥ c: t ≤ -c or t ≥ c (two half-intervals) - For |t| > c: t < -c or t > c With t = a·x + b, the solution for x is shown step by step.
- The |t| expression represents the distance of t from 0; the result is always ≥ 0.
- In the equation |t| = c, if c is negative, there is no solution (empty set).
- For |t| = c with c ≥ 0, two separate equations are written: t = c or t = -c.
- For |t| ≤ c, t is constrained to the interval: -c ≤ t ≤ c.
- When dividing by coefficient a in inequalities, the direction reverses if a < 0.
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