Subtract the first from the second: \( (2a + b) - (a + b) = -4 - (-3) \) → \( a = -1 \)

["Title: How to Solve Linear Equations: Step-by-Step Breakdown of ( (2a + b) - (a + b) = -4 - (-3) )", "Solving linear equations is a foundational skill in algebra, and understanding how to manipulate expressions step-by-step is key. One important technique is simplifying expressions by subtracting parentheses—and in this example, we’ll walk through how subtracting the first parentheses from the second leads to finding the value of ( a ).", "### The Problem: Subtracting Two Binomials", "Consider the equation:", "[\n(2a + b) - (a + b) = -4 - (-3)\n]", "At first glance, the operation involves subtracting one binomial from another and simplifying both sides before solving for ( a ). Let’s break it down carefully.", "---", "### Step 1: Distribute the Subtraction", "Subtracting a binomial requires distributing the negative sign across the terms inside the second parentheses:", "[\n(2a + b) - (a + b) = 2a + b - a - b\n]", "Notice that subtracting ( (a + b) ) is equivalent to ( -a - b ).", "---", "### Step 2: Combine Like Terms", "Now combine the like terms on the left-hand side:", "[\n2a - a + b - b = a + 0 = a\n]", "So the left side simplifies neatly to just ( a ).", "---", "### Step 3: Simplify the Right Side", "On the right-hand side, compute:", "[\n-4 - (-3) = -4 + 3 = -1\n]", "This basic arithmetic confirms the right-hand side simplifies to ( -1 ).", "---", "### Step 4: Final Equation", "Putting everything together, we now have:", "[\na = -1\n]", "---", "### Why This Matters: Algebraic Strategy", "By subtracting the first parentheses from the second and carefully combining like terms, we eliminated variables and isolated ( a ). This type of simplification is crucial when solving equations in algebra, especially in word problems or real-world modeling.", "Understanding how to simplify step-by-step—not just mechanically—builds confidence in handling more complex equations. Always remember:", "- Distribute negative signs properly\n- Combine like terms efficiently\n- Keep expressions balanced on both sides", "---", "### Practical Application", "This method applies broadly—not only in homework but in everyday math tasks like budgeting, physics formulas, or optimizing resources. Mastering the subtraction and simplification of expressions gives you a powerful tool for problem-solving.", "---", "Conclusion", "Subtracting ( (2a + b) - (a + b) ) isn’t just arithmetic—it’s strategic simplification that leads to solving for unknowns. From this step-by-step process, we find that:", "[\n(2a + b) - (a + b) = -4 - (-3) \quad \Rightarrow \quad a = -1\n]", "Keep practicing these algebraic techniques, and turn equations into clear pathways to answers.", "---", "Keywords: linear equations, algebraic manipulation, solve for ( a ), simplify expressions, step-by-step solving, subtraction of parentheses, solve ( 2a + b - (a + b) = -4 - (-3) ), algebra tutorial, finding unknown variables, math problem solving.", "---", "Start simplifying your expressions today—and unlock the power of algebraic solving!"]