["# Solving the Equation: 3(x – 4) + 2(5 – x) = 10", "When faced with an algebraic equation like 3(x – 4) + 2(5 – x) = 10, many students wonder how to simplify and solve it step-by-step. This article breaks down the process clearly, explaining each part so you can confidently solve such equations and understand the key mathematical principles involved.", "## Step 1: Expand the Brackets", "Start by eliminating the parentheses using the distributive property.", "Original equation:
\n[ 3(x – 4) + 2(5 – x) = 10 ]", "Expand both terms:
\n[ 3 \cdot x - 3 \cdot 4 + 2 \cdot 5 - 2 \cdot x = 10 ]
\n[ 3x - 12 + 10 - 2x = 10 ]", "## Step 2: Combine Like Terms", "Group the like terms together:", "[ (3x - 2x) + (-12 + 10) = 10 ]
\n[ x - 2 = 10 ]", "## Step 3: Solve for x", "Subtract 2 from both sides to isolate x:", "[ x = 10 + 2 ]
\n[ x = 12 ]", "## Final Answer:
\n[ \boxed{x = 12} ]", "---", "## Why Mistakes Happen and How to Avoid Them", "Common errors include:", "- Misapplying the distributive property
\n- Incorrectly combining constants and variables
\n- Sign errors when distributing negative signs", "Always double-check each expansion step and verify like terms carefully.", "---", "## Real-World Application", "Equations like this appear in budgeting, physics problems, or engineering calculations where balancing expressions is crucial. Solving such equations builds essential problem-solving skills applicable far beyond the classroom.", "---", "## Summary", "Solving 3(x – 4) + 2(5 – x) = 10 involves:
\n1. Expanding parentheses
\n2. Combining like terms
\n3. Isolating the variable", "With practice, this straightforward method helps develop strong algebraic intuition—key for advanced mathematics and real life.", "---", "Keywords: algebraic equation, solve 3(x – 4) + 2(5 – x) = 10, step-by-step algebra, linear equation, math tutorial, equation solving, high school math, algebra practice, basic algebra."]
