Sum: \( x + (x+2) + (x+4) = 126 \)

["# Solving the Equation: ( x + (x+2) + (x+4) = 126 ) – A Step-by-Step Guide", "Mathematics often presents problems that seem simple at first but require careful attention to detail. One such equation is:", "[\nx + (x + 2) + (x + 4) = 126\n]", "This article breaks down how to solve this linear equation step-by-step, offering clear explanations and practical insights—perfect for students, educators, and anyone looking to strengthen their algebraic skills.", "---", "## Understanding the Equation", "The equation combines three expressions involving the variable ( x ) and constants: 2 and 4 are added directly to ( x ). Simplifying this sum reveals a straightforward linear equation.", "Let’s rewrite the left-hand side:", "[\nx + (x + 2) + (x + 4)\n]", "Distribute the parentheses only if necessary, but note that in this case, the parentheses group terms clearly. Combine like terms:", "- Combine the ( x ) terms: ( x + x + x = 3x )\n- Combine the constants: ( 2 + 4 = 6 )", "So the equation simplifies to:", "[\n3x + 6 = 126\n]", "---", "## Step-by-Step Solution", "### Step 1: Isolate the variable term\nSubtract 6 from both sides to eliminate the constant on the left:", "[\n3x + 6 - 6 = 126 - 6\n]", "[\n3x = 120\n]", "### Step 2: Solve for ( x )\nDivide both sides by 3:", "[\nx = \frac{120}{3} = 40\n]", "---", "## Verifying the Solution", "Plug ( x = 40 ) back into the original equation to confirm correctness:", "[\n40 + (40 + 2) + (40 + 4) = 40 + 42 + 44 = 126\n]", "The left-hand side equals the right-hand side, confirming that ( x = 40 ) is the correct solution.", "---", "## Applications and Benefits of Solving Linear Equations", "Solving equations like ( x + (x+2) + (x+4) = 126 ) builds foundational algebraic skills essential for:", "- Real-world problem-solving: Budgeting, planning workflows, or calculating averages often rely on setting up and solving linear equations.\n- Competitive exams: Mastery of basic algebra improves performance in standardized tests such as the SAT, GRE, and math Olympiads.\n- Scientific modeling: Predicting outcomes in physics, economics, and engineering frequently uses linear relationships.", "---", "## Summary", "The equation ( x + (x + 2) + (x + 4) = 126 ) simplifies elegantly to ( 3x + 6 = 126 ), leading to a simple solution ( x = 40 ). Understanding how to simplify, isolate, and solve such expressions empowers students to tackle increasingly complex mathematical challenges confidently.", "---", "### Key Terms to Remember:\n- Like terms: Combine ( x + x + x = 3x )\n- Isolation: Move constants to balance the equation\n- Verification: Substitute back to check correctness", "---", "Mastering these steps will transform you from calculating quickly to thinking clearly—essential skills in mathematics and beyond."]