\( 3\left(\frac{34}{13}\right) + 2y = 16 \),

["# Solving the Equation: ( 3\left(\frac{34}{13}\right) + 2y = 16 )", "If you’re searching for a clear, step-by-step solution to the equation ( 3\left(\frac{34}{13}\right) + 2y = 16 ), you’ve come to the right place. This algebra problem involves understanding fractions, simplifying terms, and isolating the variable ( y )—skills essential for mastering algebra and preparing for more advanced math challenges.", "In this article, we break down how to solve the equation efficiently, explain each step clearly, and highlight practical techniques for working with fractions and linear equations.", "---", "## Step-by-Step Guide to Solve ( 3\left(\frac{34}{13}\right) + 2y = 16 )", "### Step 1: Simplify the Known Fraction\nStart by simplifying the term ( 3\left(\frac{34}{13}\right) ).\n[\n3 \cdot \frac{34}{13} = \frac{102}{13}\n]\nThis fraction is already in its simplest form, but we can leave it as ( \frac{102}{13} ) for accuracy.", "### Step 2: Rewrite the Equation\nNow substitute back into the original equation:\n[\n\frac{102}{13} + 2y = 16\n]", "### Step 3: Isolate the Variable Term\nTo isolate ( 2y ), subtract ( \frac{102}{13} ) from both sides:\n[\n2y = 16 - \frac{102}{13}\n]", "### Step 4: Convert 16 to a Fraction with Common Denominator\nExpress 16 as a fraction with denominator 13:\n[\n16 = \frac{208}{13}\n]\nNow perform the subtraction:\n[\n2y = \frac{208}{13} - \frac{102}{13} = \frac{106}{13}\n]", "### Step 5: Solve for ( y )\nDivide both sides by 2 to solve for ( y ):\n[\ny = \frac{106}{13} \div 2 = \frac{106}{13} \cdot \frac{1}{2} = \frac{106}{26}\n]\nSimplify the fraction:\n[\n\frac{106}{26} = \frac{53}{13}\n]", "---", "## Final Answer", "[\n\boxed{y = \frac{53}{13}}\n]", "---", "## What You Learned\nThis equation illustrates how to handle fractions in linear equations by:", "- Simplifying constant multiples of fractions\n- Finding a common denominator for subtraction\n- Isolating variables by systematic subtraction\n- Dividing by coefficients carefully", "Understanding these fundamentals strengthens your algebra skills, helping you tackle similar equations confidently—whether on tests, homework, or real-world problems.", "---", "## Tips for Future Equation Solving\n- Always simplify coefficients and constants before combining terms.\n- Use common denominators when dealing with fractions.\n- Isolate the variable step-by-step by undoing operations sequentially.\n- Reduce fractions to lowest terms whenever possible.", "Mastering these strategies turns complex equations into manageable steps—easily find ( y ), and the process will become faster and more intuitive!", "If you'd like more practice problems or detailed tutorials, explore our algebra lessons to build long-term math proficiency."]