Add \( (-a + b - c) + (4a + 2b + c) = 3 + 4.5 \Rightarrow 3a + 3b = 7.5 \Rightarrow a + b = 2.5 \) → (A)

["Understanding the Linear Equation: A Step-by-Step Breakdown of ( (-a + b - c) + (4a + 2b + c) = 3 + 4.5 \Rightarrow 3a + 3b = 7.5 \Rightarrow a + b = 2.5)", "Solving algebraic equations is a foundational skill in mathematics, and mastering step-by-step simplification improves both problem-solving speed and accuracy. This article walks you through the logical transformation of the equation:", "[\n(-a + b - c) + (4a + 2b + c) = 3 + 4.5\n]", "into the simplified result:", "[\na + b = 2.5\n]", "### Step 1: Simplify the Left Side", "Start by combining like terms in the left-hand side:", "[\n(-a + 4a) + (b + 2b) + (-c + c)\n]", "This yields:", "[\n3a + 3b + 0 = 3a + 3b\n]", "Note: The ( -c + c ) terms cancel out completely.", "### Step 2: Simplify the Right Side", "Conversion of the decimal sum is straightforward:", "[\n3 + 4.5 = 7.5\n]", "So now the equation becomes:", "[\n3a + 3b = 7.5\n]", "### Step 3: Factor Out Common Terms", "Factoring out the common coefficient ( 3 ) from the left-hand side improves clarity:", "[\n3(a + b) = 7.5\n]", "### Step 4: Solve for ( a + b )", "Divide both sides by 3:", "[\na + b = \frac{7.5}{3} = 2.5\n]", "---", "### Final Result", "[\na + b = 2.5\n]", "This equation is particularly useful in solving systems of equations, optimizing expressions, or analyzing linear relationships in algebra.", "---", "### Why This Equation Matters (A)", "Understanding how linear expressions combine helps in modeling real-world problems involving balances, costs, or distributions where multiple variables interact. The transformation from complex expressions to a simplified sum highlights key algebra skills valued in STEM education, engineering, economics, and computer science.", "---", "### Key Takeaways:", "- Combine like terms carefully.\n- Use cancellation when opposite terms appear (e.g., (-c + c)).\n- Factor common coefficients to simplify solutions.\n- Always verify each step for accuracy.\n- This transformation is a building block for solving more complex equations.", "---", "Try mastering this simple equation step-by-step — practice leads to fluency, and fluency leads to confidence in algebra!\n#LinearEquations #Algebra #MathSimplification #SolveEquations #aPlusbequals25"]