Let the integers be x, x+2, x+4. Their sum is 3x + 6 = 84 → 3x = 78 → x = 26.

["Understanding Integer Sequences: Solving a Simple Sum Problem with Algebra", "When tackling math problems involving sequences of integers, clear algebra and logical reasoning are key. Today, we explore a straightforward yet insightful example: finding three consecutive even integers defined as ( x ), ( x+2 ), and ( x+4 ), whose sum equals 84. By setting up a simple equation, solving for ( x ), and validating the result, we uncover a fundamental concept in algebra that applies across many mathematical challenges.", "---", "### Setting Up the Problem", "We are told that three consecutive even integers can be expressed as:\n- First integer: ( x )\n- Second: ( x+2 )\n- Third: ( x+4 )", "The sum of these three integers is given:\n[\nx + (x + 2) + (x + 4) = 84\n]", "---", "### Simplifying the Equation", "Combine like terms on the left-hand side:\n[\nx + x + 2 + x + 4 = 3x + 6\n]\nSo the equation becomes:\n[\n3x + 6 = 84\n]", "---", "### Solving for ( x )", "Subtract 6 from both sides:\n[\n3x = 84 - 6\n]\n[\n3x = 78\n]", "Now divide both sides by 3:\n[\nx = \frac{78}{3} = 26\n]", "---", "### Determining the Full Sequence", "Now that ( x = 26 ), we compute each integer:\n- First integer: ( x = 26 )\n- Second: ( x + 2 = 26 + 2 = 28 )\n- Third: ( x + 4 = 26 + 4 = 30 )", "We verify the sum:\n[\n26 + 28 + 30 = 84\n]\nThe result checks out.", "---", "### Why This Matters: The Power of Algebraic Reasoning", "This problem illustrates how variables can represent unknown quantities, and how translating real-world expressions into mathematical equations enables precise solutions. Recognizing that even consecutive even numbers follow a linear pattern allows for quick modeling:", "- Starting with any even integer ( x ),\n- Adding 2 and then adding 4 gives a sequence summing to ( 3x + 6 ),\n- Solving for ( x ) unlocks the full sequence efficiently.", "Understanding such patterns strengthens problem-solving skills applicable in number theory, competition math, and everyday real-life calculations.", "---", "### Final Answer", "Given integers ( x ), ( x+2 ), and ( x+4 ) with sum 84:\n[\n3x + 6 = 84 \Rightarrow x = 26\n]\nThus, the integers are:\n[\n\boxed{26,\ 28,\ 30}\n]", "---", "### SEO Keywords & Phrases\n- solving integer sequences,\n- algebraic method integers,\n- how to solve linear equations with integers,\n- step-by-step algebra example,\n- summing consecutive even numbers,\n- verifying integer solutions via equations.", "---", "By mastering these fundamentals, students and learners gain confidence in breaking down complex problems into manageable steps—transforming abstract numbers into clear, solvable stories."]