{"model": "claude-web", "provider": "Claude web app (claude.ai), signed in on a paid Max plan, Opus 5.5, default settings", "task": "math8-linear", "ran_at": "2026-10-17T13:44:15-0700", "prompt": "Write an 8-question quiz for 8th graders on solving linear equations in one variable, including equations with variables on both sides, distributing, and one equation with no solution and one with infinitely many solutions. Provide a step-by-step answer key.", "output": "Claude Opus 5.5\n\nI'll build this as a printable doc with the quiz first and the answer key after it.\n\nOutline's up — now writing the questions.\n\nQuestions are in — now the step-by-step answer key.\n\nThe [Linear Equations Quiz](https://claude.ai/code/artifact/e7fe99ee-0d52-409b-99a7-e40a11e534c6) is ready. You can edit it inline, export it to print, or comment if you want changes.\n\n----- ARTIFACT CONTENT (Claude Docs: \"Linear Equations Quiz – Grade 8\") -----\n\nLinear Equations Quiz – Grade 8\nOct 17, 2026 · @Leon\nQuiz\nName: ______________________  Date: ____________  Period: ______\nDirections: Solve each equation. Show all of your work. If an equation has no solution or infinitely many solutions, write that as your answer and explain how you know. Check your answers by substituting them back into the original equation.\n1. −2x + 9 = 23\n \n \n2. 5x − 4 = 2x + 14\n \n \n3. 2(3x + 1) = 4x + 16\n \n \n4. 7 − 3(x − 4) = 2x + 4\n \n \n5. 4(x + 2) = 4x + 5\n \n \n6. 2(3x − 5) + 4 = 6x − 6\n \n \n7. ½(8x − 6) = 5x − 9\n \n \n8. Gym A charges a $25 sign-up fee plus $10 per month. Gym B charges a $40 sign-up fee plus $7 per month. Write and solve an equation to find the number of months, m, after which both gyms cost the same total amount. What is that total?\n \n \nAnswer Key\nAnswers: 1) x = −7 · 2) x = 6 · 3) x = 7 · 4) x = 3 · 5) no solution · 6) infinitely many solutions · 7) x = 6 · 8) 5 months, $75.\n1. −2x + 9 = 23 → x = −7\n1. Subtract 9 from both sides: −2x = 14\n2. Divide both sides by −2: x = −7\n3. Check: −2(−7) + 9 = 14 + 9 = 23 ✓\nCommon error: dividing by 2 instead of −2 and getting x = 7.\n2. 5x − 4 = 2x + 14 → x = 6\n1. Subtract 2x from both sides: 3x − 4 = 14\n2. Add 4 to both sides: 3x = 18\n3. Divide both sides by 3: x = 6\n4. Check: 5(6) − 4 = 26 and 2(6) + 14 = 26 ✓\n3. 2(3x + 1) = 4x + 16 → x = 7\n1. Distribute the 2: 6x + 2 = 4x + 16\n2. Subtract 4x from both sides: 2x + 2 = 16\n3. Subtract 2 from both sides: 2x = 14\n4. Divide both sides by 2: x = 7\n5. Check: 2(21 + 1) = 44 and 4(7) + 16 = 44 ✓\n4. 7 − 3(x − 4) = 2x + 4 → x = 3\n1. Distribute −3 (both terms change): 7 − 3x + 12 = 2x + 4\n2. Combine like terms on the left: 19 − 3x = 2x + 4\n3. Add 3x to both sides: 19 = 5x + 4\n4. Subtract 4 from both sides: 15 = 5x\n5. Divide both sides by 5: x = 3\n6. Check: 7 − 3(3 − 4) = 7 + 3 = 10 and 2(3) + 4 = 10 ✓\nCommon error: writing −3x − 12 instead of −3x + 12 (forgetting that −3 × −4 = +12).\n5. 4(x + 2) = 4x + 5 → No solution\n1. Distribute the 4: 4x + 8 = 4x + 5\n2. Subtract 4x from both sides: 8 = 5\n3. The variable disappeared and 8 = 5 is false, so no value of x works.\nWhy: both sides have the same x-term (4x) but different constants, so they can never be equal.\n6. 2(3x − 5) + 4 = 6x − 6 → Infinitely many solutions\n1. Distribute the 2: 6x − 10 + 4 = 6x − 6\n2. Combine like terms on the left: 6x − 6 = 6x − 6\n3. Subtract 6x from both sides: −6 = −6\n4. The variable disappeared and −6 = −6 is always true, so every value of x works.\nWhy: after simplifying, both sides are identical expressions.\n7. ½(8x − 6) = 5x − 9 → x = 6\n1. Distribute ½: 4x − 3 = 5x − 9\n2. Subtract 4x from both sides: −3 = x − 9\n3. Add 9 to both sides: 6 = x\n4. Check: ½(48 − 6) = 21 and 5(6) − 9 = 21 ✓\n8. Gym word problem → 5 months, $75\n1. Write each total cost: Gym A = 25 + 10m, Gym B = 40 + 7m\n2. Set them equal: 25 + 10m = 40 + 7m\n3. Subtract 7m from both sides: 25 + 3m = 40\n4. Subtract 25 from both sides: 3m = 15\n5. Divide both sides by 3: m = 5\n6. Find the total: 25 + 10(5) = 75 and 40 + 7(5) = 75 ✓\nThe gyms cost the same, $75, after 5 months.\nSuggested scoring: 2 points per question (1 for correct work, 1 for the correct answer) = 16 points. For #5 and #6, full credit requires the simplified statement (8 = 5 or −6 = −6) and the correct conclusion.\n", "capture_note": "Claude's chat reply, then the Claude Docs document text as copied (tables copy as one cell per line; document links copy as plain text)"}