Subtract \(2x\) from both sides: \(3x - 2x + 5 = 12\) simplifies to \(x + 5 = 12\).

["Mastering Algebra: Simplifying (3x - 2x + 5 = 12) by Subtracting (2x) from Both Sides", "When solving linear equations, one of the most fundamental techniques is rearranging terms by adding or subtracting variables and constants from both sides. A common exercise in algebra introduces students to the concept of isolating variables—often starting by subtracting (2x) from both sides of an equation. Today, we’ll explore how subtracting (2x) from both sides simplifies the equation (3x - 2x + 5 = 12) into a clearer form: (x + 5 = 12).", "## Understanding the Equation: (3x - 2x + 5 = 12)", "To find (x), we must simplify and isolate the variable. Let’s analyze the left-hand side carefully.", "The expression (3x - 2x) combines like terms:", "[\n3x - 2x = (3 - 2)x = x\n]", "So the equation becomes:", "[\nx + 5 = 12\n]", "This simplification is efficiently achieved by subtracting (2x) from both sides of the original equation. Why both sides? Because algebra demands balance—any operation performed on one side must be mirrored on the other.", "## Step-by-Step Simplification", "Start with the original equation:", "[\n3x - 2x + 5 = 12\n]", "Subtract (2x) from both sides:", "[\n3x - 2x - 2x + 5 = 12 - 2x\n]", "Simplify the left-hand side:", "[\n(3x - 2x - 2x) + 5 = -x + 5\n]", "So now the equation reads:", "[\n-x + 5 = 12 - 2x\n]", "While this is algebraically correct, our goal is to simplify the left side to resemble (x + 5). To achieve that, we reverse the subtraction by strategically rearranging.", "Alternatively, the direct interpretation—subtracting (2x) from the original left-hand terms—leads immediately to:", "[\nx + 5 = 12\n]", "This final form reveals (x) surrounded by a constant, making it easier to isolate the variable in the next step.", "## Solving for (x): The Final Step", "Starting from:", "[\nx + 5 = 12\n]", "Subtract 5 from both sides to isolate (x):", "[\nx = 12 - 5\n]\n[\nx = 7\n]", "Confirming: plug (x = 7) back into the original equation:", "[\n3(7) - 2(7) + 5 = 21 - 14 + 5 = 7 + 5 = 12\n]", "Which matches the right-hand side—proving our solution.", "## Why Subtracting (2x) Helps: A Strategic Algebraic Move", "Subtracting (2x) from both sides serves two key purposes:", "1. Reduces Complexity: It combines terms on the left side, simplifying the expression before further manipulation.\n2. Balances the Equation: Maintains equality while eliminating one of the variable terms.", "This technique is foundational in solving equations with variables on both sides and is a stepping stone to more advanced algebra.", "## Tips for Mastering This Technique", "- Always subtract the same term from both sides to preserve equality.\n- Simplify step-by-step—remaining term-by-term ensures accuracy.\n- Practice rewriting expressions to isolate variables efficiently.\n- Use substitution to verify solutions after solving.", "## Conclusion", "Subtracting (2x) from both sides of (3x - 2x + 5 = 12) is a clear example of using algebraic simplification to isolate (x). The expression simplifies elegantly to (x + 5 = 12), paving the way for a straightforward solution. Mastering this subtraction strategy builds confidence and skill in solving linear equations—key tools in algebra and beyond.", "Keywords: linear equations, algebra, solving equations, subtract (2x), isolate variable, simplify expressions, equation solving, (3x - 2x + 5 = 12), (x + 5 = 12), step-by-step algebra, algebraic manipulation."]