So, \(2x + 3x + 4x = 180\).

["Solving the Linear Equation: How to Solve (2x + 3x + 4x = 180)", "Solving linear equations is a fundamental skill in algebra that forms the backbone of more advanced mathematical concepts. One common problem that students encounter is expressions like (2x + 3x + 4x = 180). Understanding how to combine like terms and isolate variables not only helps in solving equations but also sharpens logical thinking and problem-solving abilities. In this article, we’ll walk through the step-by-step solution to the equation (2x + 3x + 4x = 180), explain the algebraic principles involved, and provide tips for mastering similar problems.", "---", "### Understanding the Equation: (2x + 3x + 4x = 180)", "At first glance, (2x + 3x + 4x) appears to be a simple sum, but it’s really a collection of terms all containing the variable (x). To solve effectively, the first step is combining like terms—adding the coefficients of (x) together.", "---", "### Step 1: Combine Like Terms", "We rewrite the left-hand side of the equation by adding the coefficients:", "[\n2x + 3x + 4x = (2 + 3 + 4)x = 9x\n]", "So the equation simplifies to:", "[\n9x = 180\n]", "This reduces the original three-term equation into a straightforward linear form.", "---", "### Step 2: Isolate the Variable (x)", "To find the value of (x), divide both sides of the equation by 9:", "[\nx = \frac{180}{9} = 20\n]", "---", "### Verification: Is (x = 20) Correct?", "Always verify your solution. Substitute (x = 20) back into the original equation:", "[\n2(20) + 3(20) + 4(20) = 40 + 60 + 80 = 180\n]", "Since both sides equal 180, the solution is confirmed.", "---", "### Why This Equation Matters", "The expression (2x + 3x + 4x = 180) is more than a textbook example—it represents real-world scenarios involving proportional growth or summation. For instance:", "- If (x) represents time intervals increasing linearly, and three sequences grow by multiplying coefficients 2, 3, and 4, their cumulative sum over time reaches 180.\n- This structure appears in budgeting, physics motion problems, and resource allocation models.", "Mastering simplification and isolation techniques makes such real-life applications accessible and intuitive.", "---", "### General Strategy for Equations Like This", "Here’s a quick checklist for solving similar linear equations:", "1. Identify and combine like terms: Look for variables with the same base (here, (x)).\n2. Perform arithmetic carefully: Combine coefficients accurately.\n3. Isolate the variable: Use inverse operations—division after combining terms.\n4. Check your solution: Substitute back into the original equation.", "---", "### Summary", "- The equation (2x + 3x + 4x = 180) simplifies to (9x = 180).\n- Solving gives (x = 20).\n- Verification confirms correctness.\n- Understanding this pattern strengthens algebra proficiency and problem-solving.", "---", "### Further Practice", "Try solving more complex versions like (5x + 2(3x - 4) = 38) or (7x - 4(x + 2) = 12). With consistent practice, simplifying expressions and isolating variables becomes second nature—empowering you to tackle advanced math with confidence.", "---", "Keywords: solve linear equation, (2x + 3x + 4x = 180), combine like terms, isolate variable, algebra basics, equation solving, verify solution, real-world math applications.", "---", "Whether you're a student, teacher, or self-learner, mastering equations like (2x + 3x + 4x = 180) equips you with essential skills for academic and practical problem-solving. Start by combining terms, isolate (x), verify, and steadily build confidence in algebra!"]