\[ 3y = rac{112}{7} - rac{43}{7} \]

["3y = (112 / 7) – (43 / 7): Step-by-Step Solution and Essential Understanding", "Solving linear equations is a fundamental skill in algebra, and tackling the equation 3y = (112 / 7) – (43 / 7) offers a great opportunity to practice simplifying fractions and isolating variables. In this SEO-optimized article, we’ll break down the calculation step-by-step, explain how to simplify, and highlight the real-world relevance of solving such equations.", "---", "### Step 1: Simplify the Right-Hand Side", "Start with the equation:\n[\n3y = \frac{112}{7} - \frac{43}{7}\n]", "Both fractions have the same denominator, which makes subtraction straightforward. Since the denominators are equal, subtract numerators directly:", "[\n\frac{112 - 43}{7} = \frac{69}{7}\n]", "So now the equation becomes:\n[\n3y = \frac{69}{7}\n]", "---", "### Step 2: Isolate the Variable y", "To solve for ( y ), divide both sides by 3:\n[\ny = \frac{69}{7} \div 3\n]", "Dividing by 3 is the same as multiplying by ( \frac{1}{3} ):\n[\ny = \frac{69}{7} \ imes \frac{1}{3} = \frac{69}{21}\n]", "---", "### Step 3: Simplify the Fraction", "Now simplify ( \frac{69}{21} ): both numerator and denominator are divisible by 3:\n[\n\frac{69 \div 3}{21 \div 3} = \frac{23}{7}\n]", "Thus, the final solution is:\n[\ny = \frac{23}{7}\n]", "---", "### Alternative View: Decimal Approximation for Clarity", "For better readability, ( \frac{23}{7} ) as a decimal is approximately:\n[\n\frac{23}{7} \approx 3.2857\n]\nOr as a mixed number:\n[\ny = 3 \frac{2}{7}\n]", "---", "### Why This Equation Matters: Practical Applications", "Understanding how to simplify and solve equations like ( 3y = \frac{112}{7} - \frac{43}{7} ) applies in many real-life contexts:\n- Finance: Calculating changes in profit margins after dividing revenues and costs.\n- Science: Determining rates when subtracting measured values divided by a common unit.\n- Engineering: Solving for unknown variables in proportional systems.", "---", "### Summary", "- Simplify fractions on the right:\n[\n\frac{112}{7} - \frac{43}{7} = \frac{69}{7}\n]\n- Divide both sides by 3:\n[\ny = \frac{69}{7} \div 3 = \frac{23}{7}\n]\n- Final answer:\n[\n\boxed{y = \frac{23}{7}}\n]\n- Show decimal or mixed number equivalents for broader understanding.", "Learning to solve equations step-by-step enhances problem-solving skills essential both academically and professionally—mastering 3y = (112 / 7) – (43 / 7) is a perfect example of algorithmic thinking in action.", "---", "Keywords: solve 3y = 112/7 – 43/7, how to simplify fractions, linear equation steps, fraction division, algebraic solutions, real-world math applications.\nMeta Description: Learn step-by-step how to solve the equation ( 3y = \frac{112}{7} - \frac{43}{7} ), including simplification, variable isolation, and real-life relevance. Perfect for students and educators."]