Total: x + 1.2x + 0.9x = 3.1x = 12 → x = 12 / 3.1 ≈ <<12/3.1=3.871016129032258>>3.87 (rounded to two decimals).

["Understanding How to Solve the Equation: x + 1.2x + 0.9x = 3.1x = 12 (and Why x ≈ 3.87)", "When faced with a mathematical equation like x + 1.2x + 0.9x = 12, solving for x efficiently is key—especially for students, professionals, and anyone seeking clarity in algebra. In this article, we break down step-by-step how to simplify and solve the equation x + 1.2x + 0.9x = 12, showing exactly why x ≈ 3.87 when rounded to two decimal places.", "---", "### The Equation at a Glance\nConsider the expression:\nx + 1.2x + 0.9x = 12", "At first glance, multiple terms containing x appear added together. But in algebra, combining like terms makes the equation much easier to work with.", "---", "### Step 1: Combine Like Terms", "Notice that x, 1.2x, and 0.9x all involve the same variable. You can add their coefficients directly:\n[\nx + 1.2x + 0.9x = (1 + 1.2 + 0.9)x\n]", "Now calculate the sum:\n[\n1 + 1.2 + 0.9 = 3.1\n]", "So the equation simplifies beautifully to:\n[\n3.1x = 12\n]", "This step—combining like terms—is a fundamental skill in algebra, turning complexity into simplicity.", "---", "### Step 2: Solve for x", "Now that the equation is simplified, solve for x by dividing both sides by 3.1:\n[\nx = \frac{12}{3.1}\n]", "Using a calculator or division:\n[\nx ≈ 3.87101612903\n]", "---", "### Step 3: Rounding to Two Decimal Places", "To present the result clearly and practically, round 3.87101612903 to two decimal places.\n- Look at the third decimal digit (1), which is less than 5, so we round down.\n- The rounded value is:\n[\nx ≈ 3.87\n]", "This rounded value (3.87) is far easier to reference and interpret, especially in real-world applications like budgeting, engineering, or data analysis.", "---", "### Why This Matters: Real-World Applications of Simple Equations", "Equations like x + 1.2x + 0.9x = 12 show up in situations involving proportions, scaled growth, or resource allocation. For example:\n- calculating combined cost increases (e.g., 1x for base price, 1.2x for tax or 0.9x for commission),\n- modeling total returns based on multiple contribution rates,\n- solving for unknown quantities in scientific calculations.", "Being able to solve and interpret such equations effortlessly empowers better decision-making and problem-solving.", "---", "### Final Summary", "To solve x + 1.2x + 0.9x = 12:\n1. Combine like terms: 3.1x = 12\n2. Divide: x = 12 / 3.1\n3. Calculate and round: x ≈ 3.87", "This skill—transforming multiple parts into a single variable equation and solving cleanly—is foundational in mathematics and daily life alike. Whether you’re a student or simply enhancing arithmetic fluency, mastering this process delivers clear, confident results.", "Answer:\nx = 12 / 3.1 ≈ 3.87 (rounded to two decimal places)"]