\( 2y = 16 - \frac{102}{13} = \frac{208}{13} - \frac{102}{13} = \frac{106}{13} \),
["# Simplifying the Expression: Your Step-by-Step Guide to Solving ( 2y = 16 - \frac{102}{13} = \frac{208}{13} - \frac{102}{13} = \frac{106}{13} )", "Understanding how to simplify algebraic expressions is essential for mastering algebra. In this article, we break down the step-by-step process of solving the equation ( 2y = 16 - \frac{102}{13} ), guiding you from substitution through to simplification using clear mathematical notation and explanations.", "---", "## Step 1: Start with the Original Equation", "We begin with:", "[\n2y = 16 - \frac{102}{13}\n]", "This equation defines ( 2y ) as the difference between a whole number and a fraction.", "---", "## Step 2: Simplify the Constants on the Right Side", "To simplify ( 16 - \frac{102}{13} ), we express 16 as a fraction with denominator 13:", "[\n16 = \frac{16 \ imes 13}{13} = \frac{208}{13}\n]", "So,", "[\n16 - \frac{102}{13} = \frac{208}{13} - \frac{102}{13}\n]", "---", "## Step 3: Subtract the Fractions", "Since the denominators are the same, subtract the numerators:", "[\n\frac{208 - 102}{13} = \frac{106}{13}\n]", "Now we have:", "[\n2y = \frac{106}{13}\n]", "---", "## Step 4: Solve for ( y )", "To isolate ( y ), divide both sides of the equation by 2:", "[\ny = \frac{106}{13} \div 2 = \frac{106}{13} \ imes \frac{1}{2} = \frac{106}{26}\n]", "Simplify the fraction by dividing numerator and denominator by 2:", "[\ny = \frac{53}{13}\n]", "---", "## Final Result", "The simplified solution to the equation is:", "[\n\boxed{y = \frac{53}{13}}\n]", "---", "## Why Simplifying Linear Equations Matters", "Working through problems like ( 2y = 16 - \frac{102}{13} ) builds foundational algebra skills. Simplifying fractions and combining constants help you master:", "- Fraction arithmetic\n- Equation solving\n- Algebraic manipulation\n- Understanding rational numbers", "Whether you're studying for exams or just learning math fundamentals, mastering these steps makes complex problems easier and builds confidence in handling equations.", "---", "### Next Steps", "- Practice with different fractions and coefficients\n- Learn how to solve multi-step linear equations\n- Explore how to express answers in simplest form", "Stay tuned for more clear explanations and practice tips in upcoming algebra tutorials!", "---", "Keywords: algebra, solving equations, simplify fractions, solve for y, fractional subtraction, division by 2, rational numbers, step-by-step algebra, unsimplified to simplified, (2y = 16 - \frac{102}{13})", "---", "By mastering these steps, you’ll boost your ability to solve algebraic expressions clearly and accurately. Keep practicing — algebra rewards patience and precision!"]
