Mathematics
Absolute Value Equation / Inequality – Tutorial
On this page, you can find the logic, usage, and important details of the Absolute Value Equation / Inequality calculator.
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Summary
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.
Input Fields
Type
Type: select
Coefficient a
Type: number
Example: E.g.: 1, -2...
Constant b
Type: number
Example: E.g.: 3, -5...
Value c
Type: number
Example: E.g.: 4, 10...
Inequality type (inequality mode only)
Type: select
Decimal places
Type: number
Example: E.g.: 3, 4, 6
Advanced parameter