\( \frac{102}{13} + 2y = 16 \),

["### Solving ( \frac{102}{13} + 2y = 16 ): A Step-by-Step Guide", "If you're working through the equation ( \frac{102}{13} + 2y = 16 ), you're tackling a linear equation that combines rational numbers with a variable. Understanding how to isolate ( y ) not only helps solve the problem but also strengthens foundational algebra skills. In this article, we’ll break down how to solve this equation step-by-step, explain key concepts, and provide tips to tackle similar problems efficiently.", "---", "#### Step 1: Isolate the Variable Term", "Start by simplifying the equation to isolate the term containing ( y ).\nOriginal equation:\n[\n\frac{102}{13} + 2y = 16\n]", "Subtract ( \frac{102}{13} ) from both sides to eliminate the constant on the left side:\n[\n2y = 16 - \frac{102}{13}\n]", "---", "#### Step 2: Simplify the Right-Hand Side", "To subtract, express 16 as a fraction with denominator 13:\n[\n16 = \frac{16 \ imes 13}{13} = \frac{208}{13}\n]", "Now perform the subtraction:\n[\n2y = \frac{208}{13} - \frac{102}{13} = \frac{208 - 102}{13} = \frac{106}{13}\n]", "---", "#### Step 3: Solve for ( y )", "Now divide both sides by 2 to solve for ( y ):\n[\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:\n[\ny = \frac{53}{13}\n]", "---", "#### Final Answer", "[\n\boxed{y = \frac{53}{13}}\n]", "This is the exact solution. If desired, convert to a mixed number:\n[\n\frac{53}{13} = 4 \frac{1}{13}\n]", "---", "### Why This Problem Matters", "Solving linear equations like ( \frac{102}{13} + 2y = 16 ) builds key algebraic tools: manipulating fractions, performing arithmetic with rational numbers, and isolating variables. These skills form the backbone for more advanced math topics including systems of equations, functions, and algebraic modeling.", "---", "### Tips for Solving Similar Equations", "- Express all constants as fractions when dealing with denominators to avoid errors.\n- Keep a common denominator when subtracting rational numbers.\n- Divide carefully when isolating variables; simplifying fractions afterward reduces answer clarity.\n- Always check your solution by substituting ( y = \frac{53}{13} ) back into the original equation.", "---", "### Practice Exercise", "Try solving:\n[\n\frac{75}{26} + 3y = 10\n]", "Following the same steps, isolate ( y ) and express the solution in simplest form.", "---", "Understanding and solving equations like ( \frac{102}{13} + 2y = 16 ) transforms abstract math into a solvable puzzle—one that enhances both logical thinking and algebraic fluency. Keep practicing, and you’ll master these essential skills quickly!", "Keywords: solve linear equation, fraction arithmetic, isolate variable, algebra basics, ( \frac{102}{13} + 2y = 16 ), step-by-step algebra, rational equation solution, algebra practice."]