Their sum is \( x + (x+2) + (x+4) = 54 \).
["Finding the Sum: Solving the Equation ( x + (x+2) + (x+4) = 54 )", "When faced with the equation ( x + (x+2) + (x+4) = 54 ), solving for ( x ) is a straightforward algebraic process that reveals important mathematical principles. This equation arises frequently in algebra courses and real-world problems involving patterns and linear sequences.", "### Step-by-Step Solution", "Start by simplifying the left-hand side:", "[\nx + (x + 2) + (x + 4)\n]", "Remove parentheses and combine like terms:", "[\nx + x + 2 + x + 4 = 3x + 6\n]", "So the equation simplifies to:", "[\n3x + 6 = 54\n]", "Next, subtract 6 from both sides to isolate the term with ( x ):", "[\n3x = 48\n]", "Now, divide both sides by 3:", "[\nx = \frac{48}{3} = 16\n]", "### Verification", "Plug ( x = 16 ) back into the original expression:", "[\n16 + (16+2) + (16+4) = 16 + 18 + 20 = 54\n]", "The equation holds true, confirming the solution.", "### Why This Equation Matters", "This type of linear equation models situations where quantities increase consistently—such as total savings over time, cumulative distances, or evenly spaced measurements. Simplifying and solving ( a + (a+d) + (a+2d) = \ ext{total} ) helps develop pattern recognition and foundational algebra skills.", "### Key Takeaways", "- Combine like terms to simplify expressions.\n- Perform corresponding operations on both sides of the equation to maintain equality.\n- Always verify your solution by substituting back into the original equation.", "Understanding this simple sum equation strengthens algebraic proficiency and supports more complex problem-solving in math and everyday applications.", "---", "Keywords for SEO:\n- Solve equation ( x + (x+2) + (x+4) = 54 )\n- Algebraic solutions step-by-step\n- Linear equations with variable sums\n- How to simplify ( x + (x+2) + (x+4) )\n- Learning algebra basics\n- Real-world applications of linear equations", "Optimized meta description:\nLearn how to solve the equation ( x + (x+2) + (x+4) = 54 ) step by step—simplify, combine terms, isolate variables, and verify your answer. Perfect for students and algebra beginners."]
