The mean is \( rac{10 + 14 + 8 + 16 + x}{5} = 12 \).
["# Solving for ( x ): A Step-by-Step Guide to Finding the Unknown Value in an Average Equation", "Understanding averages is essential in math, statistics, and everyday problem-solving. One common challenge is solving equations involving the mean (average) of a set of numbers. In this article, we’ll solve the equation:", "[\n\frac{10 + 14 + 8 + 16 + x}{5} = 12\n]", "and explore how to find the unknown variable ( x ). This method is widely used in homework, tests, and real-world data analysis.", "## What Does the Mean Represent?", "The mean (or average) of a set of numbers is the sum of all values divided by the number of values. For example, if you have five numbers, the mean tells you the central value around which they cluster.", "---", "## Step 1: Rewrite the Equation Clearly", "Start with the given equation:", "[\n\frac{10 + 14 + 8 + 16 + x}{5} = 12\n]", "This means the average of five values — 10, 14, 8, 16, and an unknown ( x ) — equals 12.", "---", "## Step 2: Multiply Both Sides by 5", "To eliminate the denominator, multiply both sides of the equation by 5:", "[\n10 + 14 + 8 + 16 + x = 12 \ imes 5\n]", "[\n10 + 14 + 8 + 16 + x = 60\n]", "---", "## Step 3: Simplify the Known Numbers", "Add the constant values on the left:", "[\n10 + 14 = 24 \\n24 + 8 = 32 \\n32 + 16 = 48\n]", "So,", "[\n48 + x = 60\n]", "---", "## Step 4: Solve for ( x )", "Subtract 48 from both sides:", "[\nx = 60 - 48\n]", "[\nx = 12\n]", "---", "## Final Answer", "The value of ( x ) that makes the mean of ( {10, 14, 8, 16, x} ) equal to 12 is:", "[\n\boxed{12}\n]", "---", "## Why This Method Matters", "Using algebra to solve for unknowns in averages is a fundamental skill in mathematics and education. It applies to scoring systems, financial averages, statistical analyses, and more. Mastering these techniques enhances logical thinking and analytical capabilities.", "---", "## Summary", "- Understand that the mean is a sum divided by the count of numbers.\n- Rearrange the equation to isolate ( x ).\n- Perform arithmetic operations carefully.\n- The solution confirms ( x = 12 ).", "For further practice, try similar problems with different numbers to build fluency in solving linear equations in context.", "---", "Keywords for SEO:\nmean calculation, solve for ( x ), average equation, average example, algebra problem, math tutorial, solve linear equations, find unknown variable, math homework help, central value average, real-world statistics."]
