Simple Equations

{
  "antigravity_content": "# Unlocking the Magic of Simple Equations! \ud83c\udf89\n\nEver wanted to solve puzzles like a detective? Simple equations are your secret tools! Let\u2019s dive into the world of numbers and letters that will help you crack the code of math.\n\n---\n\n## What is a Simple Equation? \ud83e\udd14\n\n- An equation is like a balance scale.\n- It has two sides, and we need to keep them equal.\n- Simple equations can have numbers and letters (like x).\n\n### Visual Suggestion:\n- **Balance Scale Diagram:** Show a scale with numbers on both sides to illustrate balance.\n\n---\n\n## How to Solve Simple Equations \ud83d\udd75\ufe0f\u200d\u2642\ufe0f\n\n1. **Isolate the Variable (like x)**:\n   - Move numbers to the other side.\n   - Keep the equation balanced!\n  \n2. **Example**:\n   - If the equation is 2x + 3 = 11:\n     - Move 3 to the other side: 2x = 11 - 3\n     - So, 2x = 8\n     - Now, divide by 2: x = 4\n  \n3. **Think of it like gully cricket**:\n   - You need to hit the ball (the equation) in the right way to get the runs (the answer).\n\n### Visual Suggestion:\n- **Step-by-Step Flowchart:** Show the steps of moving numbers and isolating x.\n\n---\n\n## Real-Life Examples of Simple Equations \ud83d\udcb0\n\n1. **Auto-Rickshaw Fare**:\n   - If you know the fare for a distance is \u20b940 and you want to find how many kilometers (x) you can travel for \u20b9100, you can set up the equation:  \n     - 40x = 100 \u2192 x = 100/40 \u2192 x = 2.5 km\n\n2. **School Tiffin Problem**:\n   - If you have 3 samosas and want to share them equally with friends:\n   - Equation: 3 = 2x (where x is the number of friends). \n   - So, x = 3/2 \u2192 You can share them with 1.5 friends (or, you need to cut one samosa!)\n\n### Visual Suggestion:\n- **Scenario Illustrations:** Draw an auto-rickshaw and a tiffin box with samosas to make it relatable.\n\n---\n\n## Balancing Both Sides \u2696\ufe0f\n\n- Just like making chai, you need the right ingredients.\n- If you add or subtract something from one side, do the same on the other side.\n\n### Example:\n- If you have 5 + x = 12:\n  - Subtract 5 from both sides: x = 12 - 5 \u2192 x = 7.\n\n### Visual Suggestion:\n- **Chai Making Infographic:** Illustrate how balancing ingredients is like balancing an equation.\n\n---\n\n## Quick Recap! \ud83d\udcdd\n\n- **Simple equations** are like balance scales.\n- **To solve**, isolate the variable.\n- **Real-life examples** include auto fares and sharing tiffins.\n- Always **balance both sides** of the equation.\n\nKeep practicing and soon you\u0027ll be a math detective, solving mysteries with simple equations! \ud83d\udd75\ufe0f\u200d\u2640\ufe0f\u2728",
  "meta": {
    "difficulty_distribution": {
      "1": 10,
      "2": 10,
      "3": 10,
      "4": 10
    },
    "total_questions": 40
  },
  "prompt_id": null,
  "prompt_name": "Default (Anti-Gravity)",
  "questions": [
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "A simple equation includes variables like x and can be solved to find the value of those variables.",
      "id": 1,
      "options": [
        "A) An equation with only numbers",
        "B) An equation that has variables",
        "C) An equation with no solution",
        "D) An equation that cannot be solved"
      ],
      "question": "What is a simple equation?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "To isolate x, we first need to subtract 3 from both sides, resulting in 2x = 8.",
      "id": 2,
      "options": [
        "A) Add 3 to both sides",
        "B) Subtract 3 from both sides",
        "C) Multiply both sides by 2",
        "D) Divide both sides by 2"
      ],
      "question": "In the equation 2x + 3 = 11, what is the first step to isolate x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Subtracting 5 from both sides gives us x = 10 - 5, so x = 5.",
      "id": 3,
      "options": [
        "A) 15",
        "B) 5",
        "C) 10",
        "D) 0"
      ],
      "question": "If x + 5 = 10, what is the value of x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Balancing an equation means ensuring both sides have the same value.",
      "id": 4,
      "options": [
        "A) Make both sides equal",
        "B) Change one side only",
        "C) Ignore one side",
        "D) Add numbers randomly"
      ],
      "question": "What does it mean to balance an equation?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Dividing both sides by 3 gives x = 12 / 3, so x = 4.",
      "id": 5,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "In the equation 3x = 12, what is the value of x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "A variable is a symbol that represents an unknown value, such as x.",
      "id": 6,
      "options": [
        "A) 5",
        "B) x",
        "C) 10",
        "D) 15"
      ],
      "question": "Which of the following is a variable?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Subtracting 4 from both sides gives y = 9 - 4, so y = 5.",
      "id": 7,
      "options": [
        "A) 2",
        "B) 5",
        "C) 3",
        "D) 4"
      ],
      "question": "If 4 + y = 9, what is y?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "To isolate x, we add 7 to both sides to get x = 3 + 7.",
      "id": 8,
      "options": [
        "A) Add 7 to both sides",
        "B) Subtract 3 from both sides",
        "C) Multiply both sides by 7",
        "D) Divide both sides by 3"
      ],
      "question": "What is the first step in solving the equation x - 7 = 3?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Dividing both sides by 5 gives x = 25 / 5, so x = 5.",
      "id": 9,
      "options": [
        "A) 10",
        "B) 5",
        "C) 20",
        "D) 25"
      ],
      "question": "In the equation 5x = 25, what is x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 1,
      "explanation": "Subtracting 2 from both sides gives x = 4 - 2, so x = 2.",
      "id": 10,
      "options": [
        "A) 1",
        "B) 2",
        "C) 3",
        "D) 4"
      ],
      "question": "If 2 + x = 4, what is x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Adding 4 to both sides gives 6x = 30, then dividing by 6 gives x = 5.",
      "id": 11,
      "options": [
        "A) 5",
        "B) 6",
        "C) 4",
        "D) 3"
      ],
      "question": "Solve for x: 6x - 4 = 26."
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "Dividing both sides by 3 gives x + 2 = 5; subtracting 2 gives x = 3.",
      "id": 12,
      "options": [
        "A) 3",
        "B) 1",
        "C) 5",
        "D) 4"
      ],
      "question": "If 3(x + 2) = 15, what is the value of x?"
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "Subtracting 10 from both sides gives -2x = -6; dividing by -2 gives x = 3.",
      "id": 13,
      "options": [
        "A) 3",
        "B) 2",
        "C) 5",
        "D) 4"
      ],
      "question": "What is the solution to 10 - 2x = 4?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Subtracting 3 from both sides gives 5x = 15; dividing by 5 gives x = 3.",
      "id": 14,
      "options": [
        "A) 5",
        "B) 6",
        "C) 3",
        "D) 4"
      ],
      "question": "If 5x + 3 = 18, what is x?"
    },
    {
      "correct_answer": "D",
      "difficulty": 2,
      "explanation": "Adding 2 to both sides gives 4x = 12; dividing by 4 gives x = 3.",
      "id": 15,
      "options": [
        "A) 2.5",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "For the equation 4x - 2 = 10, what is the value of x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Dividing both sides by 2 gives 3x - 1 = 5; adding 1 gives 3x = 6; dividing by 3 gives x = 2.",
      "id": 16,
      "options": [
        "A) 2",
        "B) 3",
        "C) 1",
        "D) 4"
      ],
      "question": "What is the solution for the equation 2(3x - 1) = 10?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Subtracting 3 from both sides gives 8 - 3 = x, so x = 5.",
      "id": 17,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "If 8 - x = 3, what is x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "Subtracting 2 from both sides gives 7x = 28; dividing by 7 gives x = 4.",
      "id": 18,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 3"
      ],
      "question": "What is the solution to the equation 7x + 2 = 30?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Subtracting 10 from both sides gives 2x = 10; dividing by 2 gives x = 5.",
      "id": 19,
      "options": [
        "A) 5",
        "B) 10",
        "C) 15",
        "D) 0"
      ],
      "question": "If 2x + 10 = 20, what is the value of x?"
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "Subtracting 5 from both sides gives 3x = 21; dividing by 3 gives x = 7.",
      "id": 20,
      "options": [
        "A) 7",
        "B) 8",
        "C) 6",
        "D) 9"
      ],
      "question": "What is the solution for x in the equation 5 + 3x = 26?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Subtracting 4 from both sides gives 2x = 14; dividing by 2 gives x = 7.",
      "id": 21,
      "options": [
        "A) 7",
        "B) 8",
        "C) 6",
        "D) 5"
      ],
      "question": "Solve the equation 2x + 4 = 18."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Dividing both sides by 3 gives x - 4 = 3; adding 4 gives x = 7.",
      "id": 22,
      "options": [
        "A) 7",
        "B) 6",
        "C) 5",
        "D) 8"
      ],
      "question": "What is the solution to 3(x - 4) = 9?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Subtracting 9 from both sides gives 6x = 24; dividing by 6 gives x = 4.",
      "id": 23,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 3"
      ],
      "question": "In the equation 6x + 9 = 33, what is x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Dividing by 5 gives x + 1 = 6; subtracting 1 gives x = 5.",
      "id": 24,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "For the equation 5(x + 1) = 30, what is the value of x?"
    },
    {
      "correct_answer": "C",
      "difficulty": 3,
      "explanation": "Adding 3 to both sides gives 4x = 16; dividing by 4 gives x = 4.",
      "id": 25,
      "options": [
        "A) 4",
        "B) 3",
        "C) 5",
        "D) 6"
      ],
      "question": "If 4x - 3 = 13, what is x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Adding 2 to both sides gives 7x = 21; dividing by 7 gives x = 3.",
      "id": 26,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "What is the solution for 7x - 2 = 19?"
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Subtracting 9 from both sides gives -2x = -8; dividing by -2 gives x = 4.",
      "id": 27,
      "options": [
        "A) 4",
        "B) 3",
        "C) 5",
        "D) 6"
      ],
      "question": "Solve the equation 9 - 2x = 1."
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "Subtracting 4 from both sides gives 8x = 32; dividing by 8 gives x = 4.",
      "id": 28,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "If 8x + 4 = 36, what is x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Subtracting 12 from both sides gives -4x = -12; dividing by -4 gives x = 3.",
      "id": 29,
      "options": [
        "A) 2",
        "B) 3",
        "C) 4",
        "D) 5"
      ],
      "question": "What is the solution for the equation 12 - 4x = 0?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Dividing both sides by 2 gives 5x + 3 = 17; subtracting 3 gives 5x = 14; dividing by 5 gives x = 4.",
      "id": 30,
      "options": [
        "A) 4",
        "B) 3",
        "C) 2",
        "D) 1"
      ],
      "question": "If 2(5x + 3) = 34, what is the value of x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expanding gives 6x - 12 + 9 = 21; simplifying gives 6x - 3 = 21; 6x = 24; x = 4.",
      "id": 31,
      "options": [
        "A) 6",
        "B) 4",
        "C) 3",
        "D) 5"
      ],
      "question": "Solve for x: 3(2x - 4) + 9 = 21."
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Combining like terms gives x + 5 = 12; subtracting 5 gives x = 7.",
      "id": 32,
      "options": [
        "A) 5",
        "B) 6",
        "C) 4",
        "D) 3"
      ],
      "question": "What is the solution to 4x + 5 - 3x = 12?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Dividing both sides by 5 gives 2x + 1 = 7; subtracting 1 gives 2x = 6; dividing by 2 gives x = 3.",
      "id": 33,
      "options": [
        "A) 5",
        "B) 6",
        "C) 4",
        "D) 3"
      ],
      "question": "If 5(2x + 1) = 35, what is the value of x?"
    },
    {
      "correct_answer": "B",
      "difficulty": 4,
      "explanation": "Expanding gives 7x - 6x - 2 = 4; simplifying gives x - 2 = 4; x = 6.",
      "id": 34,
      "options": [
        "A) 4",
        "B) 3",
        "C) 2",
        "D) 5"
      ],
      "question": "Solve for x in the equation 7x - 2(3x + 1) = 4."
    },
    {
      "correct_answer": "C",
      "difficulty": 4,
      "explanation": "Subtracting 4 gives 2x/3 = 6; multiplying both sides by 3 gives 2x = 18; dividing by 2 gives x = 9.",
      "id": 35,
      "options": [
        "A) 8",
        "B) 6",
        "C) 7",
        "D) 5"
      ],
      "question": "What is the solution for x in the equation 2x/3 + 4 = 10?"
    },
    {
      "correct_answer": "C",
      "difficulty": 4,
      "explanation": "Subtracting 2 gives 4(x - 3) = 16; dividing by 4 gives x - 3 = 4; adding 3 gives x = 7.",
      "id": 36,
      "options": [
        "A) 3",
        "B) 4",
        "C) 6",
        "D) 5"
      ],
      "question": "If 4(x - 3) + 2 = 18, what is the value of x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Expanding gives 5x + 6 - 2x = 14; simplifying gives 3x + 6 = 14; subtracting 6 gives 3x = 8; dividing by 3 gives x = 8/3.",
      "id": 37,
      "options": [
        "A) 4",
        "B) 6",
        "C) 5",
        "D) 7"
      ],
      "question": "What is the solution for the equation 5x + 2(3 - x) = 14?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Subtracting 2x from both sides gives 4x + 2 = 18; subtracting 2 gives 4x = 16; dividing by 4 gives x = 4.",
      "id": 38,
      "options": [
        "A) 4",
        "B) 5",
        "C) 3",
        "D) 6"
      ],
      "question": "Solve for x: 6x + 2 = 2x + 18."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Expanding gives 3x + 6 = 2x + 16; subtracting 2x gives x + 6 = 16; subtracting 6 gives x = 10.",
      "id": 39,
      "options": [
        "A) 6",
        "B) 7",
        "C) 5",
        "D) 4"
      ],
      "question": "If 3(x + 2) = 2(x + 8), what is x?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "Expanding gives 8 - 6x + 8 = 0; simplifying gives -6x + 16 = 0; x = 16/6 = 8/3.",
      "id": 40,
      "options": [
        "A) 4",
        "B) 3",
        "C) 2",
        "D) 1"
      ],
      "question": "What is the solution of the equation 8 - 2(3x - 4) = 0?"
    }
  ],
  "source_ixl_skills": [],
  "topic": "Simple Equations"
}