\[ 2x + 3(3x - 5) = 12 \]

["# Solving ( 2x + 3(3x - 5) = 12 ): A Step-by-Step Guide", "Solving linear equations like ( 2x + 3(3x - 5) = 12 ) is a foundational algebra skill with applications in math, science, engineering, and everyday problem-solving. Whether you're a student learning the basics or someone looking to brush up on algebraic techniques, understanding how to simplify and solve such equations is essential. In this article, we’ll walk through the step-by-step solution of ( 2x + 3(3x - 5) = 12 ), explain key algebraic concepts, and highlight its practical significance.", "---", "## Understanding the Equation", "The given equation is:\n[\n2x + 3(3x - 5) = 12\n]", "This equation contains:", "- A linear term ( 2x )\n- A distributed term ( 3(3x - 5) ), which requires applying the distributive property\n- A constant value on the right-hand side, 12", "Mastering this type of problem helps build confidence in manipulating expressions and isolating variables—skills critical for higher-level math and real-world modeling.", "---", "## Step-by-Step Solution", "### Step 1: Expand the Parentheses Using the Distributive Property", "To eliminate the parentheses, apply the distributive property ( a(b + c) = ab + ac ):", "[\n2x + 3 \cdot 3x - 3 \cdot 5 = 12\n]\n[\n2x + 9x - 15 = 12\n]", "### Step 2: Combine Like Terms", "Combine the terms with ( x ):", "[\n(2x + 9x) - 15 = 12\n]\n[\n11x - 15 = 12\n]", "### Step 3: Isolate the Variable Term", "Add 15 to both sides to move the constant to the right:", "[\n11x = 12 + 15\n]\n[\n11x = 27\n]", "### Step 4: Solve for ( x )", "Divide both sides by 11:", "[\nx = \frac{27}{11}\n]", "---", "## The Solution", "[\n\boxed{x = \frac{27}{11}}\n]", "---", "## Why This Equation Matters", "Linear equations like ( 2x + 3(3x - 5) = 12 ) model many real-life scenarios—for example:", "- Finance: Calculating break-even points when revenue and cost functions are linear\n- Physics: Relating distance, speed, and time in motion problems\n- Economics: Determining pricing and supply-demand equilibrium\n- Education: Teaching foundational problem-solving and algebraic reasoning", "Being able to solve such equations fluently empowers learners and professionals alike to translate ambiguous problems into precise mathematical models.", "---", "## Tips for Solving Linear Equations Efficiently", "- Distribute carefully before combining like terms\n- Always isolate variable terms on one side and constants on the other\n- Check your answer by substituting ( x = \frac{27}{11} ) back into the original equation\n- Practice with varied forms to build flexible problem-solving skills", "---", "## Conclusion", "Mastering the solution of equations like ( 2x + 3(3x - 5) = 12 ) strengthens algebraic fluency and logical thinking. With careful expansion, combining terms, and isolation, even complex expressions become manageable. Whether you're preparing for exams, tackling homework, or applying math in real life, this core skill remains invaluable. Start practicing today—each equation solved brings clarity and confidence!", "---", "Keywords: ( 2x + 3(3x - 5) = 12 ), solving linear equations, algebra tricks, step-by-step solving, distributive property, isolating variables, real-life math applications", "Meta Description: Learn how to solve ( 2x + 3(3x - 5) = 12 ) step-by-step with clear explanations, practical tips, and real-world relevance. Boost your algebra skills today!"]