Question: Solve for $ x $: $ 3(x - 4) + 2(5 - x) = 10 $.
["Solve for $ x $: $ 3(x - 4) + 2(5 - x) = 10 $ – Step-by-Step Guide", "When solving linear equations, one common challenge is simplifying expressions and isolating the variable $ x $. In this article, we’ll carefully walk through how to solve the equation:", "[\n3(x - 4) + 2(5 - x) = 10\n]", "Whether you're a high school student brushing up on algebra or someone learning to master equations, this guide will clarify each step and reinforce key algebraic techniques.", "---", "### Step 1: Expand the Parentheses", "The first step is to eliminate the parentheses by distributing the constants across the terms inside. Apply the distributive property carefully:", "[\n3(x - 4) = 3 \cdot x - 3 \cdot 4 = 3x - 12\n]\n[\n2(5 - x) = 2 \cdot 5 - 2 \cdot x = 10 - 2x\n]", "Now substitute back into the equation:", "[\n3x - 12 + 10 - 2x = 10\n]", "---", "### Step 2: Combine Like Terms", "Group all the $ x $-terms and constant terms on the left side:", "[\n(3x - 2x) + (-12 + 10) = 10\n]\n[\nx - 2 = 10\n]", "---", "### Step 3: Isolate the Variable $ x $", "Add 2 to both sides to move the constant to the right:", "[\nx - 2 + 2 = 10 + 2\n]\n[\nx = 12\n]", "---", "### Step 4: Check the Solution (Optional but Recommended)", "To verify, substitute $ x = 12 $ back into the original equation:", "[\n3(12 - 4) + 2(5 - 12) = 10\n]\n[\n3(8) + 2(-7) = 10\n]\n[\n24 - 14 = 10\n]\n[\n10 = 10 \quad \checkmark\n]", "Since both sides match, the solution is correct.", "---", "### Why This Equation Matters", "Equations like $ 3(x - 4) + 2(5 - x) = 10 $ teach fundamental skills: distributing terms, combining like terms, and isolating variables. Mastering these steps helps build confidence for more complex problems in algebra and beyond—from science to finance.", "---", "### Summary", "Solving $ 3(x - 4) + 2(5 - x) = 10 $ involves:\n1. Distributing: $ 3x - 12 + 10 - 2x $\n2. Combining like terms: $ x - 2 $\n3. Solving: $ x = 12 $\n4. Verifying: Substituting back to confirm truth", "With attention to detail and practice, algebra becomes much clearer—and equations like this become a solved puzzle rather than a drain on focus.", "---", "Keywords for SEO:\nSolve linear equations, step-by-step algebra, algebra homework help, solving equations with distributive property, simplify and solve equation, $ x $ in equation, algebra tutorial, equation solving tips, step-by-step math solution", "Meta Description:\nLearn how to solve $ 3(x - 4) + 2(5 - x) = 10 $ step-by-step. Find the correct solution $ x = 12 $ with clear explanations, verification, and key algebra skills. Perfect for student learners and math enthusiasts."]
