STEM PRACTICE AND EVIDENCE WORKBENCH
Solve bounded linear-over-linear equations, enforce denominator restrictions, and audit learner solutions by direct substitution.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Cross multiply ax+b = k(x-c), collect (a-k)x = -kc-b, and calculate x = (-kc-b)/(a-k). Reject the structural case a=k in this bounded tool. Then require x different from c and substitute the learner value into the original left side. A response needs expected-value agreement, domain validity, and a residual no larger than tolerance. Supported means the entered value solves the original equation under the declared tolerance and is not excluded. A restricted entry shows why algebraic manipulation alone is insufficient. A residual conflict can identify rounding or input issues. Review the original domain before multiplying, show equivalent steps, retain exact fractions where required, and consider no-solution or identity cases with a broader method.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use after a learner has solved this bounded family of rational equations and needs independent validation of algebra and domain. The report shows the symbolic model, restriction, expected solution, and substitution residual. It does not parse arbitrary notation, handle several rational terms, classify identities when a equals k, preserve exact symbolic fractions, or replace written transformation reasoning.
Equation A solves to eight thirds and passes substitution within tolerance. Equation B solves to 1.5 and Equation C to zero. The final row has denominator restriction x different from 2 but the learner enters 2; the report blocks direct division, labels the restricted value, and shows the expected valid solution negative 2.5.
Cross multiply ax+b = k(x-c), collect (a-k)x = -kc-b, and calculate x = (-kc-b)/(a-k). Reject the structural case a=k in this bounded tool. Then require x different from c and substitute the learner value into the original left side. A response needs expected-value agreement, domain validity, and a residual no larger than tolerance.
Supported means the entered value solves the original equation under the declared tolerance and is not excluded. A restricted entry shows why algebraic manipulation alone is insufficient. A residual conflict can identify rounding or input issues. Review the original domain before multiplying, show equivalent steps, retain exact fractions where required, and consider no-solution or identity cases with a broader method.
Do not multiply only the numerator by k, distribute negative c incorrectly, divide by a-k when it is zero, cancel a term across addition, forget x=c after a factor disappears, accept a value produced by transformed work without substitution, or round before checking. State restrictions first and test candidates in the original equation.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
