STEM REASONING AND EVIDENCE WORKBENCH
Solve one-variable inequalities and make comparison-symbol reversal visible when a negative coefficient is used.
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
Remove b with an equal addition or subtraction on both sides. Divide by nonzero a. When a is positive, keep the comparison direction; when a is negative, reverse it because multiplication by a negative reverses order. The boundary is c minus b divided by a and is compared without premature rounding. A supported result requires the comparison direction and boundary to match. A boundary-only match can still describe the opposite half-line. Ask learners to test a point on each side, mark an open endpoint for strict comparison and a closed endpoint for inclusive comparison, and connect the algebra with order on a number line.
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 when learners must distinguish an equation boundary from the full inequality solution set. The diagnostic exposes whether division by a negative coefficient requires reversal. It does not parse compound inequalities, absolute values, free-form notation, interval notation, graphs, or explanations, and one item cannot diagnose stable understanding.
A positive coefficient keeps the direction, negative two reverses greater than to less than, and another positive row produces a strict upper bound. The final row divides by negative five but retains greater than or equal, so its negative-three boundary is numerically right while the represented solution set is wrong.
Remove b with an equal addition or subtraction on both sides. Divide by nonzero a. When a is positive, keep the comparison direction; when a is negative, reverse it because multiplication by a negative reverses order. The boundary is c minus b divided by a and is compared without premature rounding.
A supported result requires the comparison direction and boundary to match. A boundary-only match can still describe the opposite half-line. Ask learners to test a point on each side, mark an open endpoint for strict comparison and a closed endpoint for inclusive comparison, and connect the algebra with order on a number line.
Do not reverse the symbol after adding a negative number, forget to reverse it after multiplying or dividing by a negative, treat the boundary as the only solution, confuse < with <=, or test only the endpoint. Keep signs and operations visible and check a value from the claimed region.
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
