12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4 \Rightarrow a = \frac{4}{3}

["# Solving the Equation 12a + 3(2 - 3a) = 10: Step-by-Step Guide", "Mastering linear equations is essential for students and math enthusiasts alike. One classic example that demonstrates careful algebraic manipulation is solving the equation 12a + 3(2 - 3a) = 10. This guide walks you through the process from beginning to end, highlighting key solving techniques and explaining why each step matters. Follow along to understand how this equation leads to the solution a = \frac{4}{3}.", "---", "## The Original Equation", "Start with:", "$$\n12a + 3(2 - 3a) = 10\n$$", "This equation combines distribution and linear terms. The goal is to isolate the variable a and find its value.", "---", "## Step 1: Apply the Distributive Property", "Distribute the 3 across the parentheses:", "$$\n12a + 3 \cdot 2 - 3 \cdot 3a = 10\n$$", "$$\n12a + 6 - 9a = 10\n$$", "Why it works: The distributive property holds that c(a + b) = ca + cb, allowing us to expand the expression clearly.", "---", "## Step 2: Combine Like Terms", "Combine the terms containing a:", "$$\n(12a - 9a) + 6 = 10\n$$", "$$\n3a + 6 = 10\n$$", "Why it matters: Simplifying like terms makes the equation easier to solve and reduces errors in later steps.", "---", "## Step 3: Isolate the Variable Term", "Subtract 6 from both sides:", "$$\n3a = 10 - 6\n$$", "$$\n3a = 4\n$$", "How it helps: Isolating 3a prepares the equation for division, the next key step.", "---", "## Step 4: Solve for a", "Divide both sides by 3:", "$$\na = \frac{4}{3}\n$$", "---", "## Final Answer", "$$\na = \frac{4}{3}\n$$", "---", "## Why This Problem Matters", "Many real-world models involve linear relationships, from simple financial calculations to more complex scientific formulas. Learning to solve equations like 12a + 3(2 - 3a) = 10 builds foundational algebra skills and prepares learners for higher-level math.", "---", "## Summary of Steps", "| Step | Operation | Result |\n|-------|-----------------------------|---------------------|\n| 1 | Distribute: 3(2 - 3a) | 12a + 6 - 9a = 10 |\n| 2 | Combine like terms | 3a + 6 = 10 |\n| 3 | Subtract 6 from both sides | 3a = 4 |\n| 4 | Divide by 3 | a = 4/3 |", "---", "## Pro Tips for Solving Linear Equations", "- Always distribute any parentheses before combining like terms.\n- Keep terms organized on one side of the equation to avoid confusion.\n- Check your solution by substituting a = \frac{4}{3} back into the original equation.\n- Understand how combining like terms simplifies solutions.", "---", "Mastering these steps not only helps solve this specific equation but develops a reliable strategy for any linear equation. Whether you're a student or just brushing up on algebra, practice makes perfect!", "---", "Keywords:\n12a + 3(2 - 3a) = 10, solve linear equation, algebraic manipulation, finding 'a', step-by-step solving, algebra tutorial, solving equations, 3a = 4, fractional solution, equation simplification", "Meta Description:\nLearn how to solve 12a + 3(2 - 3a) = 10 step-by-step. Understand each algebraic move and arrive at the correct solution: a = 4/3. Perfect for students mastering basic equations."]