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sides.","code":"M"},{"id":"p2","marks":1,"description":"Correct final value for $a$.","code":"A"}],"finalAnswers":["7"],"generatedAt":"2026-05-06T14:00:08.792Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":{"methods":[{"id":"cbe8d790-425f-438d-8229-9ea80f04fd41:variables_right","label":"Grouping Variables on the Right","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\"Original Equation:\" \\quad \\htmlData{anchor=eq1}{\\color{@sky}{4a}} + 11 = \\htmlData{anchor=eq2}{\\color{@sky}{7a}} - 10$"},{"latex":"$$\"Subtract \" \\color{@sky}{4a} \" from both sides:\" \\quad 11 = \\htmlData{anchor=sub1}{\\color{@sky}{3a}} - 10$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"eq1"},{"color":"sky","style":"text-color","anchor":"eq2"},{"color":"sky","style":"text-color","anchor":"sub1"}],"connections":[{"to":"sub1","from":"eq1","color":"sky","label":"7a - 4a = 3a","style":"solid"}]},"order":0,"title":"Group variables on right","description":"To keep the coefficient of the variable $a$ positive, we choose to group the variable terms on the right side. Subtract $4a$ from both sides of the equation."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$11 = 3a - \\htmlData{anchor=const1}{\\color{@amber}{10}}$"},{"latex":"$$\"Add \" \\color{@amber}{10} \" to both sides:\" \\quad \\htmlData{anchor=const2}{\\color{@amber}{21}} = 3a$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"const1"},{"color":"amber","style":"text-color","anchor":"const2"}],"connections":[{"to":"const2","from":"const1","color":"amber","label":"11 + 10 = 21","style":"solid"}]},"order":1,"title":"Collect constant terms","description":"Next, we isolate the variable term by moving the constant term to the other side. Add $10$ to both sides of the equation to get $21 = 3a$ (which earns the first method mark M1)."},{"type":"text","order":2,"title":"Solve for a","content":"Finally, we divide both sides by the coefficient of $a$, which is $3$:\n\n$$a = \\frac{21}{3}$$\n\n$$a = 7$$\n\nThis gives us our final answer of $7$ (earning the second mark A1)."}]},{"id":"cbe8d790-425f-438d-8229-9ea80f04fd41:variables_left","label":"Grouping Variables on the Left","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4a + 11 = \blank{7a} - 10$"},{"latex":"$$\blank{4a} - \blank{7a} + 11 = -10$"},{"latex":"$$-\blank{3a} + \blank{11} = -10$"}],"highlights":[],"connections":[]},"order":0,"title":"Group variables on the left","description":"To collect all terms containing the variable $a$ on the left-hand side of the equation, we subtract $7a$ from both sides of the equation. This gives us:\n\n$$-3a + 11 = -10$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$-3a + \blank{11} = -10$"},{"latex":"$$-3a = -10 - \blank{11}$"},{"latex":"$$-3a = -21$"}],"highlights":[],"connections":[]},"order":1,"title":"Group constants on the right","description":"Now, we isolate the variable term by moving the constant term $+11$ to the right-hand side. We do this by subtracting $11$ from both sides:\n\n$$-3a = -21$$"},{"type":"text","order":2,"title":"Solve for a","content":"To find the value of $a$, we divide both sides by $-3$:\n\n$$a = \\frac{-21}{-3}$$\n\n$$a = 7$$","calculator":[{"gdc":{"instructions":"1. Open the graph application.\n2. Input the functions \$f1(x) = 4x + 11\$ and \$f2(x) = 7x - 10\$.\n3. Find the intersection of the two graphs using the Analyze Graph menu to confirm \$x = 7\$."},"ti84":{"instructions":"1. Press [Y=] and enter \$Y_1 = 4X + 11\$ and \$Y_2 = 7X - 10\$.\n2. Press [GRAPH]. Adjust window settings if necessary to see the intersection.\n3. Press [2nd] [CALC] and select '5: intersect'.\n4. Press [ENTER] three times to find the intersection point, which occurs at \$X = 7\$."},"desmos":{"instructions":"1. Type `y = 4x + 11` into the first expression bar.\n2. Type `y = 7x - 10` into the second expression bar.\n3. Click on the intersection point of the two lines to see the coordinates. The x-coordinate of the intersection point is \$7\$."},"description":"You can verify this solution by graphing both sides of the original equation, $y = 4x + 11$ and $y = 7x - 10$, and finding their point of intersection."}]}]}],"generatedAt":"2026-06-12T15:07:30.033Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":69},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/44c524d8-c025-4537-a15a-3d9a467aa35a.mp4","durationSeconds":63,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/44c524d8-c025-4537-a15a-3d9a467aa35a.jpg"}},{"id":"bce1310e-6d24-4cac-8677-3ddeaef6e58a","revisionId":"b3c288ca-154b-4111-83e9-0570814025ce","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"4b81ab03-385e-4bb1-b657-3bcabcb0540a","label":"a","content":"Solve $5(x + 4) = 33$","markscheme":"- Expands brackets or divides by 5: $5x + 20 = 33$ or $x + 4 = 6.6$ M1\n- Final answer $2.6$ or $\\frac{13}{5}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly expands brackets to get $5x + 20 = 33$ or divides both sides by 5 to get $x + 4 = 6.6$.","code":"M"},{"id":"p2","marks":1,"description":"Final correct value of $x$.","code":"A"}],"finalAnswers":["2.6","\\frac{13}{5}"],"generatedAt":"2026-05-06T14:00:09.847Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"divide_first","label":"Divide first","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\dfrac{5(x+4)}{5}=\\dfrac{33}{5}$"},{"latex":"$$x+4=6.6$"}]},"order":0,"title":"Divide both sides","description":"Divide both sides by 5 to keep the equation balanced. This gives x + 4 = 6.6 and earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x+4=6.6$"},{"latex":"$$x+4-4=6.6-4$"},{"latex":"$$x=2.6$"}]},"order":1,"title":"Subtract four","description":"Subtract 4 from both sides to leave x on its own. The correct final value earns A1."}]},{"id":"expand_first","label":"Expand first","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5(x+4)=33$"},{"latex":"$$5x+20=33$"}]},"order":0,"title":"Multiply both terms","description":"Multiply 5 by both terms inside the bracket. Expanding gives 5x + 20 = 33, which earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5x+20=33$"},{"latex":"$$5x+20-20=33-20$"},{"latex":"$$5x=13$"}]},"order":1,"title":"Subtract twenty","description":"Subtract 20 from both sides to undo the added 20."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5x=13$"},{"latex":"$$x=\\dfrac{13}{5}$"}]},"order":2,"title":"Divide by five","description":"Divide both sides by 5 to isolate x. The accepted exact answer earns A1."}]}],"generatedAt":"2026-07-19T18:51:15.248Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"4b81ab03-385e-4bb1-b657-3bcabcb0540a:expanding_brackets","label":"Expanding Brackets","steps":[{"type":"text","order":0,"title":"Expand the brackets","content":"To solve the equation using the **Expanding Brackets** method, we first multiply the term outside the bracket by each of the terms inside. \n\nMultiply $5$ by $x$, and then multiply $5$ by $4$:\n\n$$5(x + 4) = 33$$\n$$5x + 20 = 33$$\n\nThis step earns you the first mark (\\text{M1}) in the exam."},{"type":"text","order":1,"title":"Subtract 20","content":"Next, we want to isolate the $x$ term. Subtract $20$ from both sides of the equation:\n\n$$\\begin{aligned}\n5x + 20 - 20 &= 33 - 20 \\\\\n5x &= 13\n\\end{aligned}$$"},{"type":"text","order":2,"title":"Divide by 5","content":"Now, divide both sides of the equation by $5$ to solve for $x$:\n\n$$\\begin{aligned}\nx &= \\frac{13}{5} \\\\\nx &= 2.6\n\\end{aligned}$$\n\nEither the fraction $\\frac{13}{5}$ or the decimal $2.6$ is fully correct and earns you the final accuracy mark (\\text{A1})."}]},{"id":"4b81ab03-385e-4bb1-b657-3bcabcb0540a:dividing_first","label":"Dividing First","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5(x + 4) = 33$"},{"latex":"$$x + 4 = \\frac{\\htmlData{anchor=val-33}{\\color{@sky}{33}}}{\\htmlData{anchor=val-5}{\\color{@amber}{5}}}$"},{"latex":"$$x + 4 = \\htmlData{anchor=dec-val}{\\color{@purple}{6.6}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"val-33"},{"color":"amber","style":"text-color","anchor":"val-5"},{"color":"purple","style":"text-color","anchor":"dec-val"}],"connections":[{"to":"dec-val","from":"val-33","color":"purple","label":null,"style":"dashed"},{"to":"dec-val","from":"val-5","color":"purple","label":null,"style":"dashed"}]},"order":0,"title":"Divide by 5","description":"We start by dividing both sides of the equation by $5$ to isolate the expression $(x + 4)$. This gives us $x + 4 = 6.6$ (or $\\frac{33}{5}$). Performing this division earns you the first method mark (**M1**)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x + 4 = 6.6$"},{"latex":"$$x = \\htmlData{anchor=val-66}{\\color{@purple}{6.6}} - \\htmlData{anchor=val-4}{\\color{@green}{4}}$"},{"latex":"$$x = \\htmlData{anchor=ans}{\\color{@teal}{2.6}}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"val-66"},{"color":"green","style":"text-color","anchor":"val-4"},{"color":"teal","style":"text-color","anchor":"ans"}],"connections":[{"to":"ans","from":"val-66","color":"teal","label":null,"style":"solid"},{"to":"ans","from":"val-4","color":"teal","label":null,"style":"solid"}]},"order":1,"title":"Isolate the variable","description":"Next, to find $x$, subtract $4$ from both sides of the equation. This yields our final answer of $2.6$ (or $\\frac{13}{5}$ in fraction form), which completes the accuracy mark 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