y = 4\left(\frac{43}{14}\right) - 9 = \frac{172}{14} - \frac{126}{14} = \frac{46}{14} = \frac{23}{7}

["# Simplifying a Linear Expression: Y = 4 × (43/14) – 9 Step by Step", "Understanding how to simplify linear expressions is a fundamental skill in algebra. In this article, we break down the step-by-step solution to the equation:", "[ y = 4\left(\frac{43}{14}\right) - 9 ]\nand arrive at the simplified form ( y = \frac{23}{7} ). This process not only reinforces basic arithmetic and algebraic manipulation but also highlights how fractions and integers interact in equations.", "## Step 1: Multiply 4 by the Fraction", "Start by multiplying 4 with ( \frac{43}{14} ):", "[ 4 \ imes \frac{43}{14} = \frac{4 \ imes 43}{14} = \frac{172}{14} ]", "This step transforms the vision of multiplication into a single fraction, simplifying computation by reducing to one numerator and denominator.", "## Step 2: Rewrite 9 as a Fraction", "To subtract in this context, express 9 as a fraction with the same denominator as ( \frac{172}{14} ). Since 14 is the denominator, write 9 as ( \frac{126}{14} ):", "[ \frac{172}{14} - 9 = \frac{172}{14} - \frac{126}{14} ]", "Converting the whole number 9 into a fraction allows direct subtraction of numerators over the common denominator.", "## Step 3: Subtract the Fractions", "Now subtract the numerators:", "[ \frac{172}{14} - \frac{126}{14} = \frac{172 - 126}{14} = \frac{46}{14} ]", "This simplifies the expression while preserving the integrity of rational numbers.", "## Step 4: Simplify the Result", "The fraction ( \frac{46}{14} ) can be reduced by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:", "[ \frac{46 \div 2}{14 \div 2} = \frac{23}{7} ]", "This final simplified form ( \frac{23}{7} ) represents the value of ( y ), expressing the original linear expression in its simplest reduced fraction.", "## Why Simplify?\nTransforming fractions and expressions into simplest form enhances clarity, facilitates easier computation in further calculations, and is often required in standardized testing or advanced math. Recognizing patterns like integer multiplication and fraction operations speeds up algebraic reasoning.", "Whether you're solving basic equations or preparing for higher-level math, mastering these step-by-step techniques strengthens foundation and confidence in algebra.", "If you found this explanation helpful, share it with others learning algebra — understanding how to simplify linear equations opens the door to more complex mathematical problems!"]