\frac{32 + x}{60} = 0.66

["Solve the Equation: (\frac{32 + x}{60} = 0.66) – Step-by-Step Explanation", "Understanding how to solve equations involving fractions is essential for mastering algebra. One common problem students and math enthusiasts face is solving equations like (\frac{32 + x}{60} = 0.66). In this article, we’ll walk you through solving this equation step-by-step, explaining each part clearly and revealing how this equation relates to real-world applications.", "---", "### Understanding the Equation", "The equation\n[\n\frac{32 + x}{60} = 0.66\n]\nis a linear equation where a simple algebraic expression—(32 + x)—is divided by 60, resulting in 0.66. Our goal is to isolate (x) and determine its value.", "---", "### Step-by-Step Solution", "#### Step 1: Eliminate the Denominator", "To eliminate the fraction, multiply both sides of the equation by 60:\n[\n60 \cdot \frac{32 + x}{60} = 60 \cdot 0.66\n]", "Simplify both sides:\n[\n32 + x = 39.6\n]", "Note: (60 \ imes 0.66 = 39.6)", "#### Step 2: Isolate (x)", "Now, subtract 32 from both sides to solve for (x):\n[\nx = 39.6 - 32\n]\n[\nx = 7.6\n]", "---", "### Final Answer", "[\n\boxed{x = 7.6}\n]", "This means when (x = 7.6), the expression (\frac{32 + x}{60}) equals 0.66.", "---", "### Why This Equation Matters", "Equations like this appear frequently in:", "- Finance: Calculating interest rates or loan payments.\n- Engineering: Determining ratios in system designs.\n- Everyday Life: Estimating values when proportions or percentages are involved.", "---", "### How to Simplify $\frac{32 + x}{60} = 0.66$ Without Calculators", "If you need to solve it without decimal arithmetic, convert 0.66 to a fraction:\n[\n0.66 = \frac{66}{100} = \frac{33}{50}\n]\nRewriting the equation:\n[\n\frac{32 + x}{60} = \frac{33}{50}\n]", "Now cross-multiply:\n[\n50(32 + x) = 60 \cdot 33\n]\n[\n1600 + 50x = 1980\n]", "Subtract 1600:\n[\n50x = 380\n]", "Divide by 50:\n[\nx = \frac{380}{50} = 7.6\n]", "---", "### Summary", "- Multiply through by the denominator to eliminate fractions.\n- Isolate the variable using inverse operations.\n- Always verify your solution by substituting (x) back into the original equation.\n- Whether dealing with decimals or fractions, consistent simplification ensures accuracy.", "---", "Understanding this equation strengthens your algebra skills and prepares you for advanced math topics. Keep practicing with similar problems to build confidence—solve (\frac{a + x}{b} = c) anytime to master the technique!"]