Distribute and combine like terms: \(3x - 6 + 4 = 2x + 10\).
["# Distribute and Combine Like Terms: Simplify the Equation (3x - 6 + 4 = 2x + 10)", "Working with algebraic equations becomes easier when you understand how to combine like terms and distribute terms when necessary. In this article, we will explore how to simplify the equation:", "[\n3x - 6 + 4 = 2x + 10\n]", "by combining like constants and isolating the variable (x). This foundational skill is essential for solving linear equations efficiently.", "---", "## What Does “Combine Like Terms” Mean in Algebra?", "“Combining like terms” means adding or subtracting terms that have the same variable part. In this equation, the constant terms (-6) and (+4) are like terms and can be combined to simplify the expression.", "---", "## Step 1: Combine Constants on the Left Side", "Start with the left side:", "[\n3x - 6 + 4\n]", "The constant terms (-6) and (+4) combine as:", "[\n-6 + 4 = -2\n]", "So the left side becomes:", "[\n3x - 2\n]", "---", "## Step 2: Rewrite the Equation", "Now substitute the simplified left side into the original equation:", "[\n3x - 2 = 2x + 10\n]", "---", "## Step 3: Eliminate the Variable on One Side", "We want all terms with (x) on one side and constants on the other. Subtract (2x) from both sides:", "[\n3x - 2x - 2 = 2x - 2x + 10\n]", "Simplify:", "[\nx - 2 = 10\n]", "---", "## Step 4: Isolate the Variable", "Add 2 to both sides to solve for (x):", "[\nx - 2 + 2 = 10 + 2\n]", "[\nx = 12\n]", "---", "## Final Answer:", "[\n\boxed{x = 12}\n]", "---", "## Why Understanding Distribution and Combining Like Terms Matters", "Mastering the ability to simplify expressions by combining like terms and distributing (when expressions include parentheses) strengthens your algebra foundation. These skills are crucial when solving equations, understanding functions, and working on more advanced math topics like calculus and linear algebra.", "By following clear steps—identify, combine, isolate—you improve your problem-solving confidence and accuracy.", "---", "### Summary:", "- Identify and combine constants: (-6 + 4 = -2)\n- Rewrite the equation to simplify.\n- Use inverse operations to isolate (x).\n- Confirm the solution by plugging back into the original equation.", "Mastering these techniques makes solving equations faster and more intuitive. Keep practicing with different expressions to build algebra fluency!"]
