STEM PRACTICE AND EVIDENCE WORKBENCH
Solve bounded one-variable linear inequalities and expose comparison reversal, endpoint type, and number-line direction.
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
Subtract b from both sides to obtain ax compared with c minus b. Divide by a to get boundary c minus b over a. When a is negative, reverse less than with greater than and less-than-or-equal with greater-than-or-equal. Strict symbols use open endpoints; inclusive symbols use closed endpoints. Supported means both boundary and comparison direction match the solved inequality. The table translates the result into endpoint type and left or right shading for an accessible text model. Ask for substitution of one included and one excluded test value, check the original domain, and pair the text with a visual or tactile number line.
Confirm the question, source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence.
Run the worked example, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently before educational or laboratory use.
How to interpret the result
Use when sign reversal and number-line meaning need to remain visible after symbolic solving. The workbench covers one inequality with one nonzero variable coefficient. It does not parse written expressions, combine compound inequalities, apply domain restrictions, solve absolute-value or nonlinear inequalities, or draw a graphical export.
The positive-coefficient rows preserve their comparison direction after division. Negative two x plus five greater than 11 becomes x less than negative three because division by negative two reverses the sign. In the final row, negative five x plus ten greater than or equal to 25 requires x less than or equal to negative three, so the unchanged symbol is flagged.
Subtract b from both sides to obtain ax compared with c minus b. Divide by a to get boundary c minus b over a. When a is negative, reverse less than with greater than and less-than-or-equal with greater-than-or-equal. Strict symbols use open endpoints; inclusive symbols use closed endpoints.
Supported means both boundary and comparison direction match the solved inequality. The table translates the result into endpoint type and left or right shading for an accessible text model. Ask for substitution of one included and one excluded test value, check the original domain, and pair the text with a visual or tactile number line.
Do not reverse the sign when adding or subtracting, forget to reverse it when multiplying or dividing by a negative, copy the constant with the wrong sign, use a closed endpoint for a strict relation, shade toward larger values for a less-than result, or verify only the boundary. Test values on both sides.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, 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 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
