Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).

["Simplify the Equation: (2x + 12x - 15 = 6) and Solve for (x)", "Solving linear equations step-by-step is a fundamental skill in algebra—and simplifying expressions is key to finding solutions quickly and accurately. In this article, we’ll break down how to simplify the equation (2x + 12x - 15 = 6) to isolate the variable and solve for (x).", "---", "### The Equation:\n(2x + 12x - 15 = 6)", "### Step 1: Combine Like Terms\nThe first aim is simplification. Here, there are two (x)-terms: (2x) and (12x). Combine these:", "[\n(2x + 12x) - 15 = 6\n]\n[\n14x - 15 = 6\n]", "This simplification reduces complexity and speeds up the solution process.", "---", "### Step 2: Isolate the Variable Term\nNext, add 15 to both sides to move the constant term away from the (x)-term:", "[\n14x - 15 + 15 = 6 + 15\n]\n[\n14x = 21\n]", "This transformation isolates the coefficient of (x), making it easier to solve.", "---", "### Step 3: Solve for (x)\nFinally, divide both sides by 14 to solve for (x):", "[\nx = \frac{21}{14}\n]\n[\nx = \frac{3}{2}\n]", "---", "### Why Simplification Matters\nBy systematically combining like terms and isolating variables, you eliminate distractions and minimize errors—especially important when solving multi-step equations. Mastering these steps builds confidence and accuracy in algebra.", "---", "### Final Solution\n[\n\boxed{x = \frac{3}{2}}\n]", "Understanding how to simplify equations like (2x + 12x - 15 = 6) not only leads to correct answers but lays the groundwork for more advanced math topics. Practice these steps regularly, and you’ll simplify complex problems with ease.", "---", "Keywords: simplify linear equations, solve for x, algebra steps, equation solving, linear equation simplification, step-by-step algebra, how to solve 2x + 12x - 15 = 6"]