{
 "model": "openai/gpt-oss-20b",
 "provider": "Groq API (free tier)",
 "task": "math8-linear",
 "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.",
 "system": "You are helping a grade 3-8 teacher. Produce classroom-ready material.",
 "temperature": 0.3,
 "max_tokens": 6000,
 "ran_at": "2026-10-16T08:01:33-0700",
 "output": "**8th\u2011Grade Linear\u2011Equation Quiz**  \n*(Solve each equation for\u202f\\(x\\). Show all work.)*  \n\n| # | Equation | Your Work | Answer |\n|---|----------|-----------|--------|\n| 1 | \\(3x + 5 = 20\\) |  |  |\n| 2 | \\(4(x - 2) = 2x + 6\\) |  |  |\n| 3 | \\(5x - 3 = 2x + 12\\) |  |  |\n| 4 | \\(2(3x - 4) = 4x + 8\\) |  |  |\n| 5 | \\(7x + 2 = 7x - 5\\) |  |  |\n| 6 | \\(6x - 9 = 3(2x - 3)\\) |  |  |\n| 7 | \\(8 - 3x = 2x + 1\\) |  |  |\n| 8 | \\(5(2x - 1) + 3 = 4x + 11\\) |  |  |\n\n---\n\n### Answer Key \u2013 Step\u2011by\u2011Step\n\n**1.** \\(3x + 5 = 20\\)  \n\\[\n\\begin{aligned}\n3x + 5 &= 20 \\\\\n3x &= 20 - 5 \\quad (\\text{subtract }5)\\\\\n3x &= 15 \\\\\nx &= \\frac{15}{3} \\\\\nx &= 5\n\\end{aligned}\n\\]\n\n---\n\n**2.** \\(4(x - 2) = 2x + 6\\)  \n\\[\n\\begin{aligned}\n4(x - 2) &= 2x + 6 \\\\\n4x - 8 &= 2x + 6 \\quad (\\text{distribute }4)\\\\\n4x - 2x &= 6 + 8 \\quad (\\text{add }8\\text{ to both sides})\\\\\n2x &= 14 \\\\\nx &= \\frac{14}{2} \\\\\nx &= 7\n\\end{aligned}\n\\]\n\n---\n\n**3.** \\(5x - 3 = 2x + 12\\)  \n\\[\n\\begin{aligned}\n5x - 3 &= 2x + 12 \\\\\n5x - 2x &= 12 + 3 \\quad (\\text{add }3\\text{ to both sides, subtract }2x)\\\\\n3x &= 15 \\\\\nx &= \\frac{15}{3} \\\\\nx &= 5\n\\end{aligned}\n\\]\n\n---\n\n**4.** \\(2(3x - 4) = 4x + 8\\)  \n\\[\n\\begin{aligned}\n2(3x - 4) &= 4x + 8 \\\\\n6x - 8 &= 4x + 8 \\quad (\\text{distribute }2)\\\\\n6x - 4x &= 8 + 8 \\quad (\\text{subtract }4x, add }8)\\\\\n2x &= 16 \\\\\nx &= \\frac{16}{2} \\\\\nx &= 8\n\\end{aligned}\n\\]\n\n---\n\n**5.** \\(7x + 2 = 7x - 5\\) \u2013 *No solution*  \n\\[\n\\begin{aligned}\n7x + 2 &= 7x - 5 \\\\\n7x - 7x &= -5 - 2 \\quad (\\text{subtract }7x\\text{ from both sides})\\\\\n0 &= -7\n\\end{aligned}\n\\]\nSince \\(0 \\neq -7\\), the equation is impossible. **No solution.**\n\n---\n\n**6.** \\(6x - 9 = 3(2x - 3)\\) \u2013 *Infinitely many solutions*  \n\\[\n\\begin{aligned}\n6x - 9 &= 3(2x - 3) \\\\\n6x - 9 &= 6x - 9 \\quad (\\text{distribute }3)\\\\\n6x - 6x &= -9 + 9 \\quad (\\text{subtract }6x, add }9)\\\\\n0 &= 0\n\\end{aligned}\n\\]\nBoth sides are identical for every \\(x\\). **Infinitely many solutions.**\n\n---\n\n**7.** \\(8 - 3x = 2x + 1\\)  \n\\[\n\\begin{aligned}\n8 - 3x &= 2x + 1 \\\\\n8 - 1 &= 2x + 3x \\quad (\\text{add }1\\text{ to both sides, add }3x)\\\\\n7 &= 5x \\\\\nx &= \\frac{7}{5} \\\\\nx &= 1.4\n\\end{aligned}\n\\]\n\n---\n\n**8.** \\(5(2x - 1) + 3 = 4x + 11\\)  \n\\[\n\\begin{aligned}\n5(2x - 1) + 3 &= 4x + 11 \\\\\n10x - 5 + 3 &= 4x + 11 \\quad (\\text{distribute }5)\\\\\n10x - 2 &= 4x + 11 \\\\\n10x - 4x &= 11 + 2 \\quad (\\text{subtract }4x, add }2)\\\\\n6x &= 13 \\\\\nx &= \\frac{13}{6} \\\\\nx &\\approx 2.1667\n\\end{aligned}\n\\]\n\n---\n\n**Good luck, and remember to check each step for accuracy!**",
 "finish_reason": "stop",
 "usage": {
  "queue_time": 0.18084304,
  "prompt_tokens": 140,
  "prompt_time": 0.008240004,
  "completion_tokens": 1554,
  "completion_time": 1.796668645,
  "total_tokens": 1694,
  "total_time": 1.8049086490000001,
  "completion_tokens_details": {
   "reasoning_tokens": 319
  }
 },
 "retry_note": "re-run with 6000-token budget after first attempt returned empty output"
}