Solution: The average of 12, 15, and $ x $ is given by $ \frac{12 + 15 + x}{3} = 14 $. Multiply both sides by 3: $ 27 + x = 42 $. Subtract 27: $ x = 15 $. \boxed{15}

["How to Solve for $ x $ When Given the Average: A Step-by-Step Guide", "Understanding averages is a fundamental skill in mathematics, widely used in everyday calculations, statistics, and problem-solving. One common typing error in average problems occurs when miscalculating or misinterpreting the equation derived from the average formula. This article walks you through solving a classic average problem—finding the missing number $ x $—using clear, logical steps, including careful algebraic manipulation.", "---", "### Problem Statement", "We are given that the average of the numbers 12, 15, and $ x $ is 14. Set up the equation:", "[\n\frac{12 + 15 + x}{3} = 14\n]", "---", "### Step 1: Eliminate the Denominator", "To simplify the equation, multiply both sides by 3. This removes the fraction and isolates the sum of the numbers:", "[\n3 \cdot \frac{12 + 15 + x}{3} = 3 \cdot 14\n]", "Simplifying both sides gives:", "[\n12 + 15 + x = 42\n]", "---", "### Step 2: Combine Like Terms", "Add 12 and 15 together:", "[\n27 + x = 42\n]", "This step reduces the equation to a simple linear form.", "---", "### Step 3: Isolate $ x $", "Subtract 27 from both sides to solve for $ x $:", "[\nx = 42 - 27\n]", "[\nx = 15\n]", "---", "### Conclusion", "The value of $ x $ that makes the average of 12, 15, and $ x $ equal to 14 is 15. This example illustrates how basic algebra transforms word problems into solvable equations—essential for mastering averages in math and real-life applications.", "Recall:\n- The average is the sum divided by the count of numbers.\n- Always multiply both sides of an equation by the denominator to eliminate fractions.\n- Step-by-step simplification ensures accuracy and clarity.", "Mastering such steps improves your problem-solving speed and accuracy—key skills whether you're a student, educator, or just tackling math puzzles.", "---", "\boxed{15}"]