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Subtract 2k from both sides, then add 22 to both sides. Reaching 5k = 12 earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=collected_eq}{\\color{@sky}{5k=12}}$"},{"latex":"$$\\htmlData{anchor=divided_eq}{\\color{@sky}{\\dfrac{5k}{5}=\\dfrac{12}{5}}}$"},{"latex":"$$\\htmlData{anchor=fraction_answer}{\\color{@green}{k=\\dfrac{12}{5}}}$"},{"latex":"$$\\htmlData{anchor=decimal_answer}{\\color{@green}{k=2.4}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"divided_eq"},{"color":"green","style":"text-color-with-background","anchor":"decimal_answer"}],"connections":[{"to":"divided_eq","from":"collected_eq","color":"sky","label":"divide both sides by 5"},{"to":"fraction_answer","from":"divided_eq","color":"green","label":"simplify"},{"to":"decimal_answer","from":"fraction_answer","color":"green","label":"write as a decimal"}]},"order":2,"title":"Divide by five","description":"Divide both sides by the coefficient of k, which is 5. Either exact form shown is a correct final answer and earns A1."}]}],"generatedAt":"2026-07-19T18:17:02.736Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/f0c37edc-6465-4eed-a097-5c7a0d3d82f6.mp4","durationSeconds":62,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/f0c37edc-6465-4eed-a097-5c7a0d3d82f6.jpg"}},{"id":"d670f17a-eee6-417b-9b23-9431955b7759","revisionId":"bfcaf85d-5830-4a71-986b-2bc979a3b9d4","questionNumber":"17","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Solving Equations","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"97cfe6d2-b273-49cf-9842-ed9adf8fbea1","label":"a","content":"Solve $3 = 9 - 4k$","markscheme":"- Rearranges to isolate $k$ term: $4k = 6$ M1\n- Final answer $1.5$ or $\\frac{3}{2}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly isolates the $4k$ term to get $4k = 6$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $1.5$ or $\\frac{3}{2}$.","code":"A"}],"finalAnswers":["1.5","3/2"],"generatedAt":"2026-05-05T10:38:48.117Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"balance_method","label":"Balance both sides","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=eq_start}{\\color{@sky}{3=9-4k}}$"},{"latex":"$$\\htmlData{anchor=eq_add}{\\color{@sky}{3+4k=9}}$"},{"latex":"$$\\htmlData{anchor=eq_isolate}{\\color{@orange}{4k=6}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"eq_start"},{"color":"sky","style":"text-color","anchor":"eq_add"},{"color":"orange","style":"text-color-with-background","anchor":"eq_isolate"}],"connections":[{"to":"eq_add","from":"eq_start","color":"sky","style":"solid"},{"to":"eq_isolate","from":"eq_add","color":"orange","style":"solid"}]},"order":1,"title":"Isolate the term","description":"Keep the equation balanced by doing the same thing to both sides. First add 4k to both sides, then subtract 3 from both sides. Reaching 4k = 6 earns the method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=eq_start}{\\color{@sky}{4k=6}}$"},{"latex":"$$\\htmlData{anchor=eq_fraction}{\\color{@sky}{k=\\dfrac{6}{4}}}$"},{"latex":"$$\\htmlData{anchor=eq_half}{\\color{@orange}{k=\\dfrac{3}{2}}}$"},{"latex":"$$\\htmlData{anchor=eq_decimal}{\\color{@green}{k=1.5}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"eq_start"},{"color":"sky","style":"text-color","anchor":"eq_fraction"},{"color":"orange","style":"text-color","anchor":"eq_half"},{"color":"green","style":"text-color-with-background","anchor":"eq_decimal"}],"connections":[{"to":"eq_fraction","from":"eq_start","color":"sky","style":"solid"},{"to":"eq_half","from":"eq_fraction","color":"orange","style":"solid"},{"to":"eq_decimal","from":"eq_half","color":"green","style":"solid"}]},"order":2,"title":"Divide by four","description":"Divide both sides by the coefficient of k. This gives k = 6/4; simplify to k = 3/2, then convert to the decimal k = 1.5. 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Solving Equations

Question 7

Solving Equations Questions

Solving Equations

Question 7

Solving Equations Questions