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See Review policy for supplemental domain assurance." }, "internal_review": { "status": "not_applicable", "reviewer": null }, "page": "https://www.calculatorx.com/calc/math/linear-equation", "api": "https://www.calculatorx.com/api/v1/calc/linear-equation", "schema_input": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.input.json", "schema_output": "https://www.calculatorx.com/schemas/math.algebra.linear_equation.output.json", "assumptions": [ "Degree 1 only", "Not quadratic" ], "limitations": [ "Not ax² + bx + c = 0 — use /calc/math/quadratic", "Not a quadratic inequality", "Not a linear system", "Not CAS", "a = 0 and b = rhs → infinite (equation)", "a = 0 and b ≠ rhs → inconsistent (equation)", "a = 0 inequality → ℝ or ∅", "|ax+b|=rhs is mode=abs; rhs < 0 → empty", "|ax+b| ○ rhs is mode=abs_inequality; rhs < 0 → ℝ or ∅", "(ax+b)/(cx+d)=rhs is mode=rational; pole x=−d/c excluded; identically 0 denominator → INVALID_INPUT", "(ax+b)/(cx+d) ○ rhs is mode=rational_inequality; pole excluded; identically 0 denominator → INVALID_INPUT" ], "boundary_conditions": [ "missing a or rhs → MISSING_REQUIRED_INPUT", "unknown mode → INVALID_MODE" ], "sources": [ { "title": "ISO 80000-2:2019 Quantities and units — Mathematics", "url": "https://www.iso.org/standard/64973.html", "supports": "Mathematical symbols and notation. 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A denominator must be nonzero; candidates introduced by clearing denominators must be checked in the original equation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. The piecewise definition of |x|, reversal of inequalities under a negative factor, and worked absolute-value equation and inequality solutions. The calculator applies these rules to its stated linear arguments and zero/negative right-hand-side cases. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. The piecewise definition of |x|, reversal of inequalities under a negative factor, and worked absolute-value equation and inequality solutions. The calculator applies these rules to its stated linear arguments and zero/negative right-hand-side cases. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. Algebraic fraction simplification and solving linear equations, including equations with parameters and rearranging formulas. A denominator must be nonzero; candidates introduced by clearing denominators must be checked in the original equation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.", "kind": "reference", "publisher": "University of Oxford, Department of Economics; hosted by Somerville College" }, { "title": "University of Oxford Mathematical Institute — Algebra", "section": "Linear/quadratic inequalities and sign of factors", "url": "https://www.maths.ox.ac.uk/study-here/undergraduate-study/tmua/mat-livestream/algebra", "supports": "Factoring polynomials and determining sign intervals, with explicit quadratic-inequality examples. For a rational inequality the calculator applies the same factor-sign rules to numerator and denominator separately and excludes denominator zeros; that rational extension is a derived application, not a claim that the page tests this solver. 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