Set up the equation: \( x + (x+1) + (x+2) = 72 \).
["# Setting Up the Equation: ( x + (x+1) + (x+2) = 72 )", "Mathematical word problems can often seem complex at first glance, but they follow a simple structure—especially linear equations like ( x + (x+1) + (x+2) = 72 ). Setting this equation up correctly is key to solving it efficiently and accurately.", "## Understanding the Structure", "The equation ( x + (x+1) + (x+2) = 72 ) combines three terms that each contain the variable ( x ) in a sequential, increasing form. Let’s break it down:", "- The first term is simply ( x ), representing an unknown starting value.\n- The second term is ( x+1 ), indicating the next consecutive integer.\n- The third term ( x+2 ) continues the pattern, representing the next in sequence.", "These terms represent three consecutive integers starting from ( x ), summed together.", "## Step-by-Step Equation Setup", "To set up the equation step-by-step:\n1. Identify the unknown variable—here, ( x ) is the unknown.\n2. Write each term explicitly:\n [\n x + (x+1) + (x+2)\n ]\n3. Combine like terms:\n [\n x + x + 1 + x + 2 = 72\n ]\n Simplifying gives:\n [\n 3x + 3 = 72\n ]", "This final form, ( 3x + 3 = 72 ), clearly shows the equation ready for solving.", "## Why This Setup Works", "- Clarity: It explicitly shows all parts of the problem, making patterns visible.\n- Linearity: All terms are linear expressions in ( x ), simplifying manipulation.\n- Consistency: The structure aligns with standard linear equation formation—combine constants and like terms, then isolate the variable.", "## Solving the Equation (Brief Recap)", "Starting from ( 3x + 3 = 72 ):\n1. Subtract 3 from both sides:\n [\n 3x = 69\n ]\n2. Divide by 3:\n [\n x = 23\n ]", "Check the solution:\n[\n23 + 24 + 25 = 72\n]\n✅ Correct.", "## Conclusion", "Setting up the equation ( x + (x+1) + (x+2) = 72 ) correctly transforms a verbal word problem into a clear, solvable algebraic expression. By recognizing the pattern of consecutive integers, combining terms, and isolating variables, anyone can setup and solve such equations effectively—great for étudiants, self-learners, or anyone looking to sharpen math problem-solving skills.", "If you're exploring similar equations or enhancing your algebra foundation, mastering this setup is a strong first step toward confident equation solving."]
