Combine like terms: \( -15x + 5250 = 4000 \).

["Mastering Combine Like Terms: Solving ( -15x + 5250 = 4000 )", "Solving linear equations is a foundational skill in algebra, and one of the essential techniques students and learners must master is combining like terms. Whether you're simplifying expressions or solving equations, understanding how to collect and reduce terms efficiently is key to success. In this guide, we’ll break down the equation ( -15x + 5250 = 4000 ) step by step, focusing on how to combine like terms and isolate variables. Plus, we’ll explore why combining like terms is critical for accurate problem-solving in algebra.", "---", "### What Does "Combine Like Terms" Mean?", "“Like terms” are terms that contain the same variable raised to the same power—such as ( -15x ) and ( 5250 ), which both involve the variable ( x ) and constants in this context. Combining like terms means reducing or simplifying expressions by grouping these similar parts to streamline calculations. While direct combining of constants isn’t needed here until later, identifying structured terms is crucial for solving equations correctly.", "---", "### Step-by-Step Breakdown of ( -15x + 5250 = 4000 )", "Equation:\n[ -15x + 5250 = 4000 ]", "Step 1: Isolate the term with the variable\nTo begin solving for ( x ), subtract 5250 from both sides to eliminate the constant on the left side:", "[\n-15x + 5250 - 5250 = 4000 - 5250\n]\n[\n-15x = -1250\n]", "Here, we've combined constants—even though not in the traditional sense—by recognizing the full expression’s structure and simplifying one side. The left side becomes ( -15x ), and the right side is simplified to ( -1250 ).", "---", "Step 2: Solve for ( x )\nNow divide both sides by -15 to isolate ( x ):", "[\nx = \frac{-1250}{-15}\n]", "[\nx = \frac{1250}{15}\n]", "Simplifying the fraction:", "[\nx = \frac{250}{3} \quad \ ext{(exact value)}\n]", "or as a decimal:", "[\nx \approx 83.33\n]", "---", "### Why Combining Like Terms Matters", "Although the equation ( -15x + 5250 = 4000 ) didn’t require combining multi-variable like terms, understanding this concept strengthens algebraic fluency. Combining like terms simplifies expressions, reduces computational errors, and makes moving terms between sides of equations clearer. Mastering this skill prepares learners to tackle more complex expressions like:", "[\n3a + 7 + 2a - 4 = 10\n]", "where combining ( 3a ) and ( 2a ) gives ( 5a ), and ( 7 - 4 ) simplifies neatly.", "---", "### Final Answer", "The solution to ( -15x + 5250 = 4000 ) is:\n[\n\boxed{x = \frac{250}{3}} \quad \ ext{(exact)},\quad \approx 83.33 \quad \ ext{(decimal approximation)}\n]", "---", "### Tips for Practicing Combined Like Terms", "- Always identify variable terms and constants separately.\n- Rewrite expressions to bring like terms together before combining.\n- Use cancellation to simplify both sides of an equation.\n- Practice with real-world word problems to see the technique applied dynamically.\n- Always verify solutions by plugging them back into the original equation.", "---", "Mastering combine like terms isn’t just about algebra—it’s about building logic, precision, and confidence to solve equations efficiently. With consistent practice, this core skill becomes second nature, paving the way for advanced math success.", "---", "Keywords: combine like terms, algebra tutorial, solve linear equation, combine like terms definition, step-by-step equation solving, solve (-15x + 5250 = 4000), simplifying expressions, algebraic proficiency, algebra basics.\nMeta Description: Learn how to combine like terms while solving (-15x + 5250 = 4000) step-by-step. Master essential algebra skills with clear examples and pro tips."]