\( 2x + 3(10 - x) = 100 \)

["Solve ( 2x + 3(10 - x) = 100 ) – A Step-by-Step Guide", "Understanding how to solve linear equations like ( 2x + 3(10 - x) = 100 ) is essential for mastering algebra and tackling real-world problems. In this SEO-optimized guide, we’ll walk through solving this equation clearly, explain each step, and highlight why mastering such equations matters. Whether you're a student, teacher, or self-learner, this breakdown helps boost your problem-solving skills.", "---", "### What Is the Equation ( 2x + 3(10 - x) = 100 )?", "The expression ( 2x + 3(10 - x) = 100 ) is a linear equation involving both variables and constants. Solving it means finding the value of ( x ) that makes the equation true. This type of problem often appears in algebra classes and serves as a foundation for more advanced math.", "---", "### Why Solve Linear Equations?", "Linear equations like ( 2x + 3(10 - x) = 100 ) model everyday situations: budgeting, physics, and optimization problems. Mastering them improves critical thinking and analytical skills—valuable in STEM fields, economics, and everyday decision-making.", "---", "### Step-by-Step Solution", "Let’s solve ( 2x + 3(10 - x) = 100 ) step-by-step.", "#### Step 1: Expand the Parentheses\nDistribute the 3 across ( (10 - x) ):\n[\n2x + 3 \cdot 10 - 3 \cdot x = 100\n]\n[\n2x + 30 - 3x = 100\n]", "#### Step 2: Combine Like Terms\nCombine the ( x )-terms:\n[\n(2x - 3x) + 30 = 100\n]\n[\n- x + 30 = 100\n]", "#### Step 3: Isolate the Variable\nSubtract 30 from both sides:\n[\n- x = 100 - 30\n]\n[\n- x = 70\n]", "#### Step 4: Solve for ( x )\nMultiply both sides by -1 to find ( x ):\n[\nx = -70\n]", "---", "### Interpretation & Verification", "Plugging ( x = -70 ) back into the original equation confirms correctness:\n[\n2(-70) + 3(10 - (-70)) = -140 + 3(80) = -140 + 240 = 100\n]\nThe equation holds true.", "---", "### Real-World Applications\nThis equation could model, for example, a cost scenario where ( x ) represents a variable quantity, such as:", "- ( 2x ): cost scaled to some factor\n- ( 3(10 - x) ): a fixed or during-time cost component\n- ( 100 ): total budget or constraint", "Understanding how ( x ) balances these components helps in planning and optimization.", "---", "### Tips for Solving Similar Equations", "- Always expand parentheses before combining terms.\n- Carefully collect like terms (( x )-terms and constants).\n- Isolate ( x ) using inverse operations.\n- Always verify your solution by substituting back.\nUse these strategies to efficiently tackle expressions like ( 5(2x - 3) + x = 70 ) or ( 4x - 7(3 - x) = 50 ).", "---", "### Conclusion", "Mastering linear equations by solving ( 2x + 3(10 - x) = 100 ) strengthens algebraic reasoning and problem-solving. This foundational skill equips learners to interpret and solve real-world challenges confidently. Keep practicing—each equation brings you closer to fluency in mathematics.", "---", "Keywords:\nlinear equations, solve (2x + 3(10 - x) = 100), algebra tutorial, solve linear equations step-by-step, algebra problem solving, equation verification, real-world math applications, solve equations online, math problem solver, algebra basics", "Meta Description:\nLearn how to solve ( 2x + 3(10 - x) = 100 ) with a clear step-by-step guide. Master algebra fundamentals, verify your solution, and understand real-world applications—ideal for students and educators.", "Dwell Time Encouragement:\nTake practice problems and boost your algebra skills—every equation opens the door to deeper understanding!", "---", "Start solving smarter today—linear equations await!"]