STEM REASONING AND EVIDENCE WORKBENCH
Solve ax plus b equals c equations, expose inverse-operation steps, and audit learner solutions and reasoning claims.
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
For ax plus b equals c with nonzero a, subtract b from both sides to obtain ax equals c minus b, then divide both sides by a. The unique solution is x equals c minus b divided by a. The engine substitutes and compares values at full precision while auditing the claimed first step independently. A supported row has both a matching inverse step and numeric solution. A solution-only match can hide unsupported work, while a correct first step with a wrong result suggests a later arithmetic or sign issue. Ask the learner to show both sides and verify the original equation rather than assigning a permanent label.
Confirm the question, approved source, units, notation, signs, response coding, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner evidence.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, representation, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use for a bounded diagnostic after learners have studied balancing linear equations. It separately checks the first inverse operation and final numeric solution. It does not parse free-form equations, prove why equality is preserved, grade written work, handle identities or contradictions, or infer a misconception from one response.
Three rows correctly undo the constant and solve for x, including a negative coefficient and fractional solution. The final learner correctly proposes subtracting ten but reports x equals one for 5x plus 10 equals negative 5; substitution shows the result should be negative three, so the row remains flagged.
For ax plus b equals c with nonzero a, subtract b from both sides to obtain ax equals c minus b, then divide both sides by a. The unique solution is x equals c minus b divided by a. The engine substitutes and compares values at full precision while auditing the claimed first step independently.
A supported row has both a matching inverse step and numeric solution. A solution-only match can hide unsupported work, while a correct first step with a wrong result suggests a later arithmetic or sign issue. Ask the learner to show both sides and verify the original equation rather than assigning a permanent label.
Do not move terms by changing signs without explaining an equal operation, divide only one term, lose a negative coefficient, round a fraction too early, or verify against a transformed expression only. Preserve equality, use parentheses, simplify carefully, and substitute into the original equation.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish a chemical structure, or replace teacher, laboratory, 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 school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
