"grey","points":[{"x":610,"y":88},{"x":610,"y":112}]},{"id":"tick_6","type":"line","color":"grey","points":[{"x":740,"y":88},{"x":740,"y":112}]},{"id":"tick_7","type":"line","color":"grey","points":[{"x":805,"y":88},{"x":805,"y":112}]},{"x":90,"y":130,"id":"label_m4","gap":8,"size":"s","text":"−4","type":"text","anchorTo":"tick_m4","orientation":"below"},{"x":155,"y":130,"id":"label_m3","gap":8,"size":"s","text":"−3","type":"text","anchorTo":"tick_m3","orientation":"below"},{"x":220,"y":130,"id":"label_m2","gap":8,"size":"s","text":"−2","type":"text","anchorTo":"tick_m2","orientation":"below"},{"x":285,"y":130,"id":"label_m1","gap":8,"size":"s","text":"−1","type":"text","anchorTo":"tick_m1","orientation":"below"},{"x":350,"y":130,"id":"label_0","gap":8,"size":"s","text":"0","type":"text","anchorTo":"tick_0","orientation":"below"},{"x":415,"y":130,"id":"label_1","gap":8,"size":"s","text":"1","type":"text","anchorTo":"tick_1","orientation":"below"},{"x":480,"y":130,"id":"label_2","gap":8,"size":"s","text":"2","type":"text","anchorTo":"tick_2","orientation":"below"},{"x":545,"y":130,"id":"label_3","gap":8,"size":"s","text":"3","type":"text","anchorTo":"tick_3","orientation":"below"},{"x":610,"y":130,"id":"label_4","gap":8,"size":"s","text":"4","type":"text","anchorTo":"tick_4","orientation":"below"},{"x":740,"y":130,"id":"label_6","gap":8,"size":"s","text":"6","type":"text","anchorTo":"tick_6","orientation":"below"},{"x":805,"y":130,"id":"label_7","gap":8,"size":"s","text":"7","type":"text","anchorTo":"tick_7","orientation":"below"},{"h":20,"w":20,"x":665,"y":90,"id":"open_circle","geo":"ellipse","fill":"none","type":"geo","color":"blue"},{"x":675,"y":130,"id":"label_5","gap":10,"size":"s","text":"5","type":"text","anchorTo":"open_circle","orientation":"below"}],"caption":"Values smaller than $5$ lie to its left. **B1:** Arrow or line pointing to the left from the circle."}]}],"generatedAt":"2026-07-19T16:38:11.227Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"ff94a843-bcf8-4873-adaf-44b82faa3d7c","label":"b","content":"$$-3 \\leq y < 1$ where $y$ is an integer.\n\nWrite down all the possible values of $y$.","markscheme":"- Lists values: $-3, -2, -1, 0$ B2\n- Award B1 for 3 correct values and no more than 1 incorrect value.","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":2,"description":"List all four correct values: $-3, -2, -1, 0$. Award 1 mark for 3 correct values and no more than 1 incorrect value.","code":"B"}],"finalAnswers":["-3, -2, -1, 0"],"generatedAt":"2026-05-06T14:03:26.696Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"integer_number_line","label":"Read the integer bounds","steps":[{"type":"text","order":0,"title":"Read the lower bound","content":"The inequality $-3\\leq y$ means that $y$ can equal $-3$ or be greater than $-3$. Because $y$ must be an integer, start the list at $-3$.","highlights":[{"text":"$$-3 \\leq y < 1$","location":"specification"},{"text":"where $y$ is an integer.","location":"specification"}]},{"type":"text","order":1,"title":"List the integers","content":"Count upwards in consecutive integers from $-3$, stopping before $1$:\n\n$$y=-3,\\,-2,\\,-1,\\,0$$\n\nAll four values: **2 marks**. Three correct values and no more than one incorrect value: **1 mark**.","highlights":[{"text":"$$-3 \\leq y < 1$ where $y$ is an integer.","location":"specification"}]}]}],"generatedAt":"2026-07-19T16:40:33.845Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"1f77f7dd-3612-4517-bdc9-1427b6e22828","label":"c","content":"Solve $6x + 8 \\leq 2x + 28$","markscheme":"- Subtracts $2x$ from both sides: $4x + 8 \\leq 28$ M1\n- Subtracts 8 from both sides: $4x \\leq 20$ M1\n- Final answer: $x \\leq 5$ A1","marks":3,"order":2,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Subtracts $2x$ from both sides resulting in $4x + 8 \\leq 28$.","code":"M"},{"id":"p2","marks":1,"description"

Inequalities Questions

Inequalities Questions

Inequalities Questions

Inequalities Questions