Question:** Solve for \(x\) in the equation \(3x - 5 = 2x + 7\).
["How to Solve (3x - 5 = 2x + 7) – Step-by-Step Guide", "If you're learning algebra, one of the first equations you’ll encounter is a linear equation like (3x - 5 = 2x + 7). Solving for (x) is a fundamental skill that builds confidence and problem-solving abilities—especially useful in math exams, homework, or real-world applications.", "This guide breaks down how to solve the equation (3x - 5 = 2x + 7) clearly and efficiently.", "---", "### What Does the Equation Mean?", "The equation (3x - 5 = 2x + 7) states that two expressions are equal. Our goal is to isolate (x) on one side to find its exact value.", "---", "### Step-by-Step Solution", "Step 1: Get all (x)-terms on one side", "Subtract (2x) from both sides to eliminate it from the right side:", "[\n3x - 5 - 2x = 2x + 7 - 2x\n]", "Simplify:", "[\nx - 5 = 7\n]", "Step 2: Isolate the variable", "Now, add 5 to both sides to move the constant term:", "[\nx - 5 + 5 = 7 + 5\n]", "Simplify:", "[\nx = 12\n]", "---", "### Final Answer", "The solution to the equation (3x - 5 = 2x + 7) is\n[\n\boxed{x = 12}\n]", "---", "### Why This Equation Matters", "- It demonstrates balance: what you do to one side, you must do to the other to maintain equality.\n- It reinforces key algebraic techniques: combining like terms, using inverse operations.\n- It’s a foundational skill used in more complex equations, word problems, and real-world modeling.", "---", "### How to Verify the Answer", "Plug (x = 12) back into the original equation:", "Left side:\n(3(12) - 5 = 36 - 5 = 31)", "Right side:\n(2(12) + 7 = 24 + 7 = 31)", "Since both sides equal 31, the solution is verified.", "---", "### Common Mistakes to Avoid", "- Forgetting to simplify both sides after performing operations\n- Moving only one term or constant instead of balancing both sides\n- Rushing the process without checking each step", "---", "### Practice Makes Perfect", "Try solving similar equations:\n- (5x + 3 = 2x - 4)\n- (4x - 7 = 3x + 2)\n- And mix constants and coefficients for more complex challenges.", "---", "### Summary", "Solving (3x - 5 = 2x + 7) teaches essential algebraic strategies:", "- Subtract or add terms to isolate (x),\n- Balance both sides carefully,\n- Always verify your solution.", "With consistent practice, you’ll quickly become comfortable solving linear equations—key to mastering algebra.", "#SolveForX #AlgebraTutorial #LinearEquations #MathHelp #StudentResources #AlgebraSkills"]
