\[ 3y = rac{69}{7} \] - United Radiology

["# Solving the Equation: 3y = 69/7 – A Step-by-Step Guide", "Understanding how to solve linear equations is essential for mastering algebra. In this article, we’ll explore how to solve the equation 3y = 69/7, step by step, while highlighting useful techniques and real-world applications. Whether you're a student, educator, or math enthusiast, this breakdown will help you confidently tackle similar equations.", "---", "## What Does 3y = 69/7 Mean?", "The equation 3y = 69/7 is a simple linear equation where variable y is multiplied by 3 and equals a fraction. Solving for y means finding the value of y that makes both sides equal. This skill builds a strong foundation for algebra and more advanced mathematics.", "---", "## Step-by-Step Solution", "### Step 1: Isolate the Variable y
\nTo solve for y, divide both sides of the equation by 3:", "[
\n3y = \frac{69}{7}
\n]", "[
\ny = \frac{69}{7} \div 3
\n]", "### Step 2: Rewrite Division as Multiplication by the Reciprocal
\nDividing by 3 is the same as multiplying by 1/3:", "[
\ny = \frac{69}{7} \ imes \frac{1}{3}
\n]", "### Step 3: Multiply the Fractions
\nMultiply the numerators and denominators:", "[
\ny = \frac{69 \ imes 1}{7 \ imes 3} = \frac{69}{21}
\n]", "### Step 4: Simplify the Fraction
\nFind the greatest common divisor (GCD) of 69 and 21. The GCD is 3:", "[
\n\frac{69 \div 3}{21 \div 3} = \frac{23}{7}
\n]", "---", "## Final Answer", "[
\ny = \frac{23}{7}
\n]", "This can also be expressed as a decimal:
\n[
\ny \approx 3.2857
\n]", "---", "## Why This Equation Matters", "Linear equations like 3y = 69/7 appear frequently in real-world scenarios, such as:", "- Budgeting: Calculating costs or savings over time.
\n- Distance and Speed: Finding time taken given distance and velocity.
\n- Science: Solving for quantities in chemical or physical formulas.", "Mastering these basic algebraic steps not only boosts math proficiency but also empowers problem-solving across disciplines.", "---", "## Practice Time", "Try solving similar equations:
\n- 2x = 36/5 → x = ?
\n- 5y = 85/2 → y = ?", "Applying the same method will strengthen your algebraic intuition.", "---", "## Frequently Asked Questions (FAQs)", "Q: How do I divide by 3 in 3y = 69/7?
\nA: Dividing by 3 is equivalent to multiplying by 1/3.
\nQ: Can I leave the answer as a fraction?
\nA: Yes—the simplified fractional form is clean and precise. Decimals are useful for approximations.", "---", "## Conclusion", "Solving 3y = 69/7 teaches key algebraic skills with a clear, manageable example. By isolating y, simplifying fractions, and reducing steps, solving linear equations becomes intuitive. Keep practicing—each equation brings you closer to mastery!", "---", "Keywords for SEO:
\n3y = 69/7, solve linear equation, algebraic equations, fraction division, step-by-step algebra, fractional solution, how to solve 3y = 69/7, simplify 3y equation, real-world math problems", "Meta Description:
\nLearn how to solve 3y = 69/7 step-by-step. Understand fraction division, simplify expressions, and apply algebra to real-life problems with clear examples. Ideal for students and learners."]