This fixed three-item activity connects the transformed comparison, boundary inclusion, interval, number line, and substitution checks. I1 becomes x > −5; I2 changes the original symbol to ≤ and becomes x ≥ −5; I3 divides a positive coefficient and becomes x < 5. The HTML game keeps responses attached to each item and checks the chosen transformation and boundary together.
Explain the negative division
I1 starts with −4x < 20. Dividing both sides by −4 reverses the comparison, producing x > −5. OpenStax's linear inequalities lesson explains that sign-aware operation and the corresponding solution-set representations.
Use x = 1 as a check in the original statement: −4 < 20 is true. The proposed set x < −5 excludes 1, so it cannot describe the solution. That concrete contradiction gives the learner something to explain beyond being told to reverse a sign.
The other supplied checks are x = −6, giving 24 < 20, false, and x = −5, giving 20 < 20, also false. The boundary value is excluded because the comparison is strict.
Match the number line to the statement
For x > −5, draw an open boundary at −5 and shade toward greater values. The interval is (−5,∞), and the text description is all real values greater than −5.
The arrow indicates that the set continues beyond the picture. The right edge of the displayed line is not an endpoint of the solution, and infinity is not a selectable finite value. Keep the written inclusion statement available alongside the graphic.
The game asks learners to choose both a transformed statement and Open or Closed. Checking one field alone would miss a learner who finds the direction but includes an excluded boundary. Written reasoning remains for the teacher to review.
Change strict to inclusive
I2 uses −4x ≤ 20. Dividing by negative four still reverses direction, but the result is x ≥ −5. Now the boundary is closed, and the interval is [−5,∞).
At x = −5, substitution gives 20 ≤ 20, true. The −6 and 1 checks remain false and true respectively. This one boundary test explains exactly what changes between I1 and I2.
Switching items updates the original inequality, answer choices, interval context, and test ledger. It also clears the previous item's visible feedback before showing the current item's own blank or retained response. An accepted I1 answer should never appear as an accepted I2 answer by accident.
Compare positive division
I3 starts with 4x < 20. Dividing by positive four preserves the direction, giving x < 5, an open boundary, leftward shading, and interval (−∞,5).
The candidate checks are 4, 5, and 6. They produce 16 < 20, true; 20 < 20, false; and 24 < 20, false. Ask why the sign rule differs from I1 even though both problems divide to isolate x.
Use the original inequality to check the chosen set. These three supplied items need no arbitrary-expression solver. A zero coefficient would require a different pathway; division by zero is not a valid extension.
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Build a single-file US-English HTML inequality reasoning game with three fixed items. Use an original number-line challenge design, minimum 16px text, readable mathematical labels, and a 360px responsive layout. Include local code only, no expression parser, network, scores, or persistence.
I1 is -4x < 20. Correct transformation x > -5, open boundary -5, shade right, interval (-5,infinity). Substitution ledger: -6 gives 24 < 20 false; -5 gives 20 < 20 false; 1 gives -4 < 20 true. Include x < -5 as a distractor and explain why x=1 contradicts it.
I2 is -4x <= 20. Correct x >= -5, closed boundary, right shading, interval [-5,infinity). Tests -6 false, -5 true, 1 true. I3 is 4x < 20. Correct x < 5, open boundary 5, left shading, interval (-infinity,5). Tests 4 true, 5 false, 6 false. Explain negative division reverses direction while positive division preserves it.
Provide item-selection buttons, independently labeled transformation and Open/Closed choices, a blank explanation, and type=button Check. Start unanswered. Match both choices; distinguish missing responses from wrong direction or boundary. Give structural feedback and reveal the matching interval, original substitutions, and original number line plus equivalent text. Reasons are teacher-reviewed, not automatically graded.
Switch items without transferring choices or accepted feedback; retained attempts must belong to their IDs. Editing clears stale feedback. Reset clears all three. Repeated checks do not add items. The graphic's arrow continues beyond its viewport and infinity is not a finite endpoint. Do not divide by zero or add unsupported inequality types. Return complete accessible HTML using explicit selectors.
Prepare the comparison by trying the wrong-direction option and the I2 boundary before class. Preview the HTML in NOS to inspect its number line and substitutions together. Keep the lesson handout and learner explanations, then ask which tested value proves whether the boundary belongs.