Simple Equations

{
  "antigravity_content": "### Lesson on Simple Equations\n\n**Objective:** Understand the basics of simple equations and how to solve them step-by-step.\n\n---\n\n**1. Can you do this? Quick Check!**\n\nLet\u0027s start by checking your understanding. Can you solve this simple equation?\n\n\\[ x + 5 = 12 \\]\n\nWhat would you do to solve for \\( x \\)?\n\n*(Wait for the child to respond. If they seem unsure, continue guiding them)*\n\n---\n\n**2. Introduction to Equations**\n\nAlgebra is like solving a puzzle! You have numbers, letters, and symbols, and your job is to find the secret value of the letters. \n\n**What is an equation?**  \nAn equation states that two things are equal, usually involving a variable, like \\( x \\).\n\n---\n\n**3. I Do: Showing the Process**\n\nLet\u0027s look at the equation we checked earlier:\n\n\\[ x + 5 = 12 \\]\n\nTo solve for \\( x \\), we want to isolate it on one side. Here\u0027s how I would do it:\n\n- **Step 1:** Subtract 5 from both sides to keep the equation balanced.\n  \n  \\[\n  x + 5 - 5 = 12 - 5\n  \\]\n\n- **Step 2:** This simplifies to:\n\n  \\[\n  x = 7\n  \\]\n\nNow, \\( x \\) is isolated, and we found that \\( x = 7 \\).\n\n---\n\n**4. We Do: Guided Practice**\n\nNow let\u2019s try another one together. \n\n**Example:** Solve \\( x - 3 = 10 \\).\n\n- **Step 1:** What operation do we need to do to both sides to isolate \\( x \\)?\n\n*(Encourage them to respond)*\n\n- **Step 2:** Right! We need to add 3 to both sides. Let\u2019s do it together:\n\n  \\[\n  x - 3 + 3 = 10 + 3\n  \\]\n\n  What does that give us?\n\n*(Wait for the child to respond)*\n\n- If they need a hint: \"Remember, when you add something to both sides, you keep them equal!\"\n\n---\n\n**5. You Do: Independent Practice**\n\nNow it\u2019s your turn! Solve this equation on your own:\n\n\\[ x + 8 = 15 \\]\n\nTake your time, and remember the steps we practiced!\n\n*(Wait, observe, and guide if necessary. Celebrate their effort whether they solve it correctly or not)*\n\n---\n\n**6. Celebrate Effort!**\n\nGreat job working through that! Whether you got it right or needed a little help, what matters is that you tried and used your strategy. \n\n---\n\n**7. Wrap Up**\n\nToday, we learned how to solve simple equations by isolating the variable. Remember, algebra is like solving a puzzle, and every step you take gets you closer to finding the answer. \n\nNext time, we can explore more complex equations or different algebraic concepts! What do you think you\u0027d like to learn next? \n\n*(Encourage their input and interest in the next topic)*",
  "meta": {
    "difficulty_distribution": {
      "1": 10,
      "2": 10,
      "3": 10,
      "4": 10
    },
    "total_questions": 40
  },
  "prompt_id": "zpd_adaptive",
  "prompt_name": "\ud83c\udfaf ZPD Adaptive Tutor (Research: Vygotsky 1978)",
  "questions": [
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "To solve x + 3 = 10, subtract 3 from both sides: x = 10 - 3, so x = 7.",
      "id": 1,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "Solve for x: x + 3 = 10"
    },
    {
      "correct_answer": "C",
      "difficulty": 1,
      "explanation": "To find x, add 4 to both sides: x = 5 + 4, so x = 9.",
      "id": 2,
      "options": [
        "A) 1",
        "B) 5",
        "C) 9",
        "D) 10"
      ],
      "question": "What is the value of x in the equation x - 4 = 5?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Divide both sides by 2: x = 14 / 2, so x = 7.",
      "id": 3,
      "options": [
        "A) 5",
        "B) 7",
        "C) 10",
        "D) 12"
      ],
      "question": "Find x: 2x = 14"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Subtract 7 from both sides: x = 15 - 7, so x = 8.",
      "id": 4,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Solve x + 7 = 15."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Subtract 2 from both sides: x = 10 - 2, so x = 8.",
      "id": 5,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "What is the value of x in the equation 10 = x + 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Add 6 to both sides: x = 4 + 6, so x = 10.",
      "id": 6,
      "options": [
        "A) 8",
        "B) 10",
        "C) 12",
        "D) 14"
      ],
      "question": "Find the value of x in x - 6 = 4."
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Subtract 3 from both sides: x = 9 - 3, so x = 6.",
      "id": 7,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Solve for x: 3 + x = 9."
    },
    {
      "correct_answer": "D",
      "difficulty": 1,
      "explanation": "Divide both sides by 5: x = 25 / 5, so x = 5.",
      "id": 8,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is x if 5x = 25?"
    },
    {
      "correct_answer": "C",
      "difficulty": 1,
      "explanation": "Subtract 12 from both sides: x = 20 - 12, so x = 8.",
      "id": 9,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "Solve x + 12 = 20."
    },
    {
      "correct_answer": "D",
      "difficulty": 1,
      "explanation": "Add 1 to both sides: x = 8 + 1, so x = 9.",
      "id": 10,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "Find the value of x in 8 = x - 1."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Subtract 3 from both sides: 2x = 8, then divide by 2: x = 4.",
      "id": 11,
      "options": [
        "A) 4",
        "B) 3",
        "C) 5",
        "D) 6"
      ],
      "question": "Solve for x: 2x + 3 = 11."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Add 5 to both sides: 3x = 15, then divide by 3: x = 5.",
      "id": 12,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 7"
      ],
      "question": "What is x in the equation 3x - 5 = 10?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Divide both sides by 4: x + 2 = 8, then subtract 2: x = 6.",
      "id": 13,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "Find x if 4(x + 2) = 32."
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "Subtract 4 from both sides: x/3 = 4, then multiply by 3: x = 12.",
      "id": 14,
      "options": [
        "A) 9",
        "B) 10",
        "C) 12",
        "D) 15"
      ],
      "question": "Solve for x: x/3 + 4 = 8."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Add 15 to both sides: 5x = 15, then divide by 5: x = 3.",
      "id": 15,
      "options": [
        "A) 1",
        "B) 3",
        "C) 5",
        "D) 6"
      ],
      "question": "What is the value of x in 5x - 15 = 0?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Subtract 7 from both sides: 2x = 16, then divide by 2: x = 8.",
      "id": 16,
      "options": [
        "A) 8",
        "B) 9",
        "C) 10",
        "D) 11"
      ],
      "question": "Find x in the equation 7 + 2x = 23."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Add 10 to both sides: 4 = 2x - 14, then add 14: 18 = 2x, divide by 2: x = 9.",
      "id": 17,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "Solve x - 10 = 3x - 14."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Divide both sides by 6: x - 1 = 5, then add 1: x = 6.",
      "id": 18,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "What is the value of x if 6(x - 1) = 30?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Subtract 4 from both sides: 6 = 2x, then divide by 2: x = 3.",
      "id": 19,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "Find x in 10 = 2x + 4."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Subtract 5 from both sides: 2x = 14, then divide by 2: x = 7.",
      "id": 20,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "Solve for x in the equation 5 + 2x = 19."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Divide by 3: x + 2 = 7, then subtract 2: x = 5.",
      "id": 21,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Solve for x: 3(x + 2) = 21."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Subtract 2 from both sides: 4x = 16, then divide by 4: x = 4.",
      "id": 22,
      "options": [
        "A) 4",
        "B) 3",
        "C) 2",
        "D) 5"
      ],
      "question": "What is the value of x in 4x + 2 = 18?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Subtract 4: 2(x - 3) = 6, divide by 2: x - 3 = 3, add 3: x = 6.",
      "id": 23,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Find x in 2(x - 3) + 4 = 10."
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Subtract 2x: 3x - 3 = 6, add 3: 3x = 9, divide by 3: x = 3.",
      "id": 24,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "Solve for x: 5x - 3 = 2x + 6."
    },
    {
      "correct_answer": "C",
      "difficulty": 3,
      "explanation": "Subtract 7: -3x = -6, divide by -3: x = 2.",
      "id": 25,
      "options": [
        "A) 1",
        "B) 2",
        "C) 3",
        "D) 4"
      ],
      "question": "What is the value of x if 7 - 3x = 1?"
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Expand: 4x + 3 = 2x + 10, subtract 2x: 2x + 3 = 10, subtract 3: 2x = 7, divide by 2: x = 3.",
      "id": 26,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "Solve for x: 4x + 3 = 2(x + 5)."
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Expand: 6x - 5 = 3x + 3, subtract 3x: 3x - 5 = 3, add 5: 3x = 8, divide by 3: x = 2.",
      "id": 27,
      "options": [
        "A) 1",
        "B) 2",
        "C) 3",
        "D) 4"
      ],
      "question": "Find x in 6x - 5 = 3(x + 1)."
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Expand: 8 - 2x - 6 = 0, simplify: 2 - 2x = 0, add 2x: 2 = 2x, divide by 2: x = 1.",
      "id": 28,
      "options": [
        "A) 1",
        "B) 2",
        "C) 3",
        "D) 4"
      ],
      "question": "Solve for x: 8 - 2(x + 3) = 0."
    },
    {
      "correct_answer": "C",
      "difficulty": 3,
      "explanation": "Subtract 5: 10x = 30, then divide by 10: x = 3.",
      "id": 29,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the value of x if 10x + 5 = 35?"
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Expand: 2x + 8 = 3x - 2, subtract 2x: 8 = x - 2, add 2: x = 10.",
      "id": 30,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Find x in 2(x + 4) = 3x - 2."
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expand: 6x - 3 + 4 = 10, simplify: 6x + 1 = 10, subtract 1: 6x = 9, divide by 6: x = 3.",
      "id": 31,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "Solve for x: 3(2x - 1) + 4 = 10."
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expand: 4x - 8 = 6x + 2, add 8: 4x = 6x + 10, subtract 4x: -2x = 10, divide by -2: x = 5.",
      "id": 32,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the value of x in 4(x - 2) = 2(3x + 1)?"
    },
    {
      "correct_answer": "C",
      "difficulty": 4,
      "explanation": "Expand: 5 + 3x - 3 = 2x + 7, simplify: 3x + 2 = 2x + 7, subtract 2x: x + 2 = 7, subtract 2: x = 5.",
      "id": 33,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "Solve for x: 5 + 3(x - 1) = 2x + 7."
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Divide by 7: 2x + 3 = 6, subtract 3: 2x = 3, divide by 2: x = 3.",
      "id": 34,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the value of x if 7(2x + 3) = 42?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Expand: 6x - 6x + 8 = 10, simplify: 8 = 10, which is not possible.",
      "id": 35,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "Find x in 6x - 2(3x - 4) = 10."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Expand: 4x + 1 = 6x - 3, subtract 4x: 1 + 3 = 2x, add 2: 4 = 2x, divide by 2: x = 2.",
      "id": 36,
      "options": [
        "A) 1",
        "B) 2",
        "C) 3",
        "D) 4"
      ],
      "question": "Solve for x: 4x + 1 = 3(2x - 1)."
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expand: 6x + 2 = 4x + 6, subtract 4x: 2x + 2 = 6, subtract 2: 2x = 4, divide by 2: x = 2.",
      "id": 37,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the value of x if 2(3x + 1) = 4x + 6?"
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expand: 2x + 6 + 4 = 3x - 2, simplify: 2x + 10 = 3x - 2, subtract 2x: 10 = x - 2, add 2: x = 12.",
      "id": 38,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 7"
      ],
      "question": "Find x in 2(x + 3) + 4 = 3x - 2."
    },
    {
      "correct_answer": "C",
      "difficulty": 4,
      "explanation": "Expand: 9x - 4 = 6x + 10, subtract 6x: 3x - 4 = 10, add 4: 3x = 14, divide by 3: x = 14/3.",
      "id": 39,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the value of x if 9x - 4 = 2(3x + 5)?"
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Subtract 5: 5 = 2(x - 2), divide by 2: 5/2 = x - 2, add 2: x = 5/2 + 2.",
      "id": 40,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "Solve for x: 10 = 5 + 2(x - 2)."
    }
  ],
  "source_ixl_skills": [],
  "topic": "Simple Equations"
}