["# Solving ( 3x + 4x + 5x = 60 ): A Step-by-Step Guide for Beginners", "Solving linear equations is a foundational skill in algebraic mathematics. One of the simplest yet classic examples is the equation ( 3x + 4x + 5x = 60 ). Whether you're a student learning algebra or someone brushing up on basic math, understanding how to solve this equation step by step can boost your confidence and problem-solving skills.", "This article will walk you through solving ( 3x + 4x + 5x = 60 ), explain why combining like terms is essential, and offer tips to master such equations in no time.", "---", "## Understanding the Equation", "The equation given is:", "[
\n3x + 4x + 5x = 60
\n]", "Here, ( x ) is a variable representing an unknown number, and the equation balances both sides by stating that the sum of these multiplied variables equals 60.", "---", "## Step 1: Combine Like Terms", "The first and most crucial step in solving the equation is combining like terms. The terms ( 3x ), ( 4x ), and ( 5x ) all contain the same variable ( x ), so we can add their coefficients:", "[
\n3x + 4x + 5x = (3 + 4 + 5)x = 12x
\n]", "So the original equation simplifies to:", "[
\n12x = 60
\n]", "This simplification makes the equation much easier to solve.", "---", "## Step 2: Isolate the Variable ( x )", "To solve for ( x ), divide both sides of the simplified equation by the coefficient of ( x ), which is 12:", "[
\nx = \frac{60}{12}
\n]", "[
\nx = 5
\n]", "---", "## Step 3: Verify the Solution", "To ensure the solution is correct, substitute ( x = 5 ) back into the original equation:", "[
\n3(5) + 4(5) + 5(5) = 15 + 20 + 25 = 60
\n]", "The left side equals 60, which matches the right side of the equation—this confirms the solution is accurate.", "---", "## Why Combining Like Terms Matters", "Combining like terms reduces complexity and makes equations easier to solve. Instead of dealing with separate multipliers, algebra lets us sum coefficients, streamlining calculations and reducing the chance of error.", "---", "## Common Mistakes to Avoid", "- Forgetting to add coefficients correctly (e.g., ( 3 + 4 = 7 ), not ( 3×4 ))
\n- Dividing incorrectly or forgetting to isolate ( x )
\n- Not verifying the solution by plugging it back into the original equation", "---", "## Real-Life Applications", "Equations like ( 3x + 4x + 5x = 60 ) model real-world situations, such as calculating total costs (with different pricing units), distributing items evenly, or setting up budgets. Mastering these steps builds a strong foundation for more advanced math and problem-solving skills.", "---", "## Frequently Asked Questions (FAQ)", "Q: Why is combining like terms necessary?
\nA: It simplifies expressions by reducing redundant calculations and makes solving equations faster and clearer.", "Q: What does ( x = 5 ) mean in this context?
\nA: The value 5 is the unknown quantity that makes the original equation true.", "Q: Can I solve this without combining like terms?
\nA: Technically, yes—but it’s more cumbersome. Breaking down the problem step by step makes it easier to follow and less error-prone.", "---", "## Summary", "Solving ( 3x + 4x + 5x = 60 ) involves:", "1. Combining like terms to simplify the equation to ( 12x = 60 )
\n2. Dividing both sides by the coefficient of ( x ) to isolate ( x )
\n3. Verifying the solution by substitution", "This straightforward problem exemplifies key algebraic techniques that apply to more complex equations. With practice, you’ll build confidence in manipulating and solving linear equations efficiently.", "---", "Learn more about algebra basics, equation solving tips, and practice problems by exploring our full guide on linear equations. Start simplifying your math today!"]
