\frac{8a + 12}{3} = 15

["Solving (\frac{8a + 12}{3} = 15): A Step-by-Step Guide", "Understanding how to solve equations like (\frac{8a + 12}{3} = 15) is essential for mastering algebra. Whether you're preparing for exams, doing homework, or simply building strong foundations in math, knowing how to work through this equation step by step is key. In this article, we’ll break down the solution clearly and explain it in a way that boosts your learning and helps you remember the process.", "---", "### What Does the Equation Mean?", "The expression (\frac{8a + 12}{3} = 15) represents a proportion: the value of (8a + 12), divided by 3, equals 15. To solve for (a), we want to isolate the variable on one side of the equation. This process clears fractions and simplifies the expression using basic algebraic rules.", "---", "### Step 1: Eliminate the Denominator", "We start by multiplying both sides of the equation by 3 to eliminate the denominator:", "[\n3 \cdot \frac{8a + 12}{3} = 3 \cdot 15\n]", "Simplifying both sides gives:", "[\n8a + 12 = 45\n]", "This step removes the fraction and isolates the linear expression involving (a).", "---", "### Step 2: Subtract 12 from Both Sides", "Next, subtract 12 from both sides to isolate the term with (a):", "[\n8a + 12 - 12 = 45 - 12\n]", "Simplifying:", "[\n8a = 33\n]", "This simplifies our equation cleanly, leaving only the term with the variable.", "---", "### Step 3: Divide Both Sides by 8", "To solve for (a), divide both sides of (8a = 33) by 8:", "[\na = \frac{33}{8}\n]", "---", "### Final Answer", "[\na = 4.125\n]", "You can express the answer as a fraction (\frac{33}{8}) or as a decimal 4.125, depending on context.", "---", "### Why This Matters: Real-World Applications", "Understanding equations like (\frac{8a + 12}{3} = 15) helps in many practical scenarios — from solving for unknown quantities in science and engineering to interpreting data in business and everyday calculations. Breaking equations down step by step strengthens your ability to analyze problems logically and precisely.", "---", "### Summary", "Solving (\frac{8a + 12}{3} = 15) involves:", "- Clearing the fraction by multiplying both sides by 3\n- Isolating the linear expression by subtracting constants\n- Solving for the variable by dividing", "With practice, this method becomes intuitive and builds a strong foundation in algebra.", "---", "Ready to practice more? Try solving similar equations like (\frac{5x - 7}{2} = 10) to build your confidence and sharpen your algebra skills!", "---", "Keywords: solve linear equation, algebra, solve (\frac{8a + 12}{3} = 15), step-by-step algebra, isolate variable, linear equations, math tutorial"]