THE NUMORIX GUIDE
How to use the Compound Inequality Calculator
Last reviewed September 14, 2026
What this calculator does
The current engine interprets the four inputs as the single strict inequality lowerCoeff*x+lowerConst < upperCoeff*x+upperConst, rearranges to (lowerCoeff-upperCoeff)*x < upperConst-lowerConst, and flips the sign when dividing by a negative coefficient difference.
Formula and method
The current engine interprets the four inputs as the single strict inequality lowerCoeff*x+lowerConst < upperCoeff*x+upperConst, rearranges to (lowerCoeff-upperCoeff)*x < upperConst-lowerConst, and flips the sign when dividing by a negative coefficient difference.
Variables and inputs
The defaults are lower side 1*x-3 and upper side 1*x+9. UI labels are left coefficient/constant and right coefficient/constant; all inequalities are strict.
Worked example
With defaults: coefficient difference = 1-1=0 and constant difference = 9-(-3)=12; 0*x<12 is true for every real x, so the engine returns (-infinity,infinity). With 2x+1 < x+7, it gives x<6.
How to interpret the result
The result is an open interval, all real numbers, or no solution for the exact inequality interpretation used by this route.
Common mistakes to avoid
Do not read the labels as a conventional lower bound < x < upper bound; the engine compares two linear expressions. Remember that dividing an inequality by a negative reverses its direction.
Assumptions and limitations
The source comments mention a different a < x+b < c interpretation, but the implemented code solves the two-expression inequality. It does not expose <=, >=, or a standalone bounded compound form.
Practical use and checks
Use the Compound Inequality Calculator only after reading the exact algebraic form represented by its coefficient fields. For lower coefficient 2, lower constant 0, upper coefficient 1, and upper constant 6, the engine rearranges 2x < x + 6 and should return x < 6. That check makes the sign flip logic visible: if the coefficient difference is negative, dividing by it changes the inequality direction. A valid open interval should not include its endpoint because the comparison is strict. There is an important implementation edge on this route. The default-looking inputs lower coefficient 1, lower constant -3, upper coefficient 1, and upper constant 9 produce an identity -3 < 9 after the x terms cancel, so the engine reports all real numbers, not the familiar interval -3 < x < 9 that the page wording may suggest. Treat the displayed steps as authoritative and verify the intended inequality separately before using a bound for a safety limit or eligibility rule. Zero coefficient difference can mean all values or no values depending on the constants; a negative divisor flips the comparison. The calculator does not support every compound-inequality notation, inclusive endpoints, unions, or domain restrictions.