\[ y = 4 imes rac{43}{14} - 9 = rac{172}{14} - rac{126}{14} = rac{46}{14} = rac{23}{7} \].

["# Mastering Linear Equations: Solving ( y = 4 \ imes \frac{43}{14} - 9 ) Step-by-Step", "Understanding how to solve linear equations is a foundational skill in algebra, essential for high school students, educators, and anyone looking to strengthen their math proficiency. One common task is solving expressions like:", "[\ny = 4 \ imes \frac{43}{14} - 9\n]", "In this article, we’ll break down the solution comprehensively and explain each step in detail—perfect for mastering linear expressions and simplifying fractions.", "---", "## Step 1: Begin with the Original Expression", "Start with the full equation:", "[\ny = 4 \ imes \frac{43}{14} - 9\n]", "This equation defines ( y ) in terms of a fractional multiplication and a subtraction. The key to solving this lies in simplifying the arithmetic step by step.", "---", "## Step 2: Multiply 4 by ( \frac{43}{14} )", "Since 4 = ( \frac{4}{1} ), we multiply:", "[\n4 \ imes \frac{43}{14} = \frac{4 \ imes 43}{14} = \frac{172}{14}\n]", "Why this works: When multiplying fractions with integer numerators, we multiply numerators together and denominators together. Here, ( 4 \ imes 43 = 172 ), and ( 1 \ imes 14 = 14 ), so the result is ( \frac{172}{14} ).", "---", "## Step 3: Rewrite the Subtraction Term Using a Common Denominator", "Now rewrite ( 9 ) as a fraction with denominator 14 to subtract easily:", "[\n9 = \frac{9 \ imes 14}{14} = \frac{126}{14}\n]", "Why this is useful: Subtracting fractions requires a common denominator. Expressing 9 as ( \frac{126}{14} ) enables direct subtraction from ( \frac{172}{14} ).", "---", "## Step 4: Perform the Subtraction", "Now subtract:", "[\ny = \frac{172}{14} - \frac{126}{14} = \frac{172 - 126}{14} = \frac{46}{14}\n]", "Simplification insight: The difference of numerators gives a simplified fraction, but we can do more.", "---", "## Step 5: Simplify the Fraction ( \frac{46}{14} )", "Both 46 and 14 are divisible by 2:", "[\n\frac{46 \div 2}{14 \div 2} = \frac{23}{7}\n]", "This is the final simplified form.", "---", "## Final Result: ( y = \frac{23}{7} )", "Thus:", "[\ny = 4 \ imes \frac{43}{14} - 9 = \frac{23}{7}\n]", "---", "## Why This Process Matters", "Breaking down expressions like this helps reinforce key concepts:", "- Order of operations (PEMDAS/BODMAS)\n- Fraction multiplication and simplification\n- Common denominators for subtraction", "These skills are vital not only in algebra but in real-world applications involving ratios, rates, and proportions.", "---", "## Tip for Quick Calculations", "Consider simplifying before multiplying:\nSince ( \frac{43}{14} \approx 3.071 ), multiplying ( 4 \ imes \frac{43}{14} ) gives approximately ( 12.2857 ), which subtracting 9 yields about 3.2857 — matching ( \frac{23}{7} \approx 3.2857 ). This verifies our exact result with a real-world check.", "---", "## Conclusion", "Solving ( y = 4 \ imes \frac{43}{14} - 9 ) step-by-step turns a seemingly complex equation into an accessible algebra challenge. By handling fractions carefully, using common denominators, and simplifying results, you build confidence and accuracy—key habits for mastering math.", "If you found this guide helpful, share it with fellow learners and practice similar problems daily. Mastery comes from practice, and algebra is no exception!", "---", "Keywords:\nlinear equations, solve algebra, simplify fractions, ( y = 4 \ imes \frac{43}{14} - 9 ), fraction multiplication, simplifying expressions, algebra step-by-step, rational numbers, ( \frac{23}{7} ), mathematical problem solving.", "---", "Meta Description:\nLearn how to solve ( y = 4 \ imes \frac{43}{14} - 9 ) step-by-step. Understand fraction multiplication, simplification, and conversion to final answer ( \frac{23}{7} )—perfect for algebra beginners."]