Solve for \(x\) in the equation \(3x + 5 = 2x + 12\).

["How to Solve for (x) in the Equation (3x + 5 = 2x + 12)", "Solving algebraic equations is a fundamental skill in mathematics, and one of the most common types involves linear equations with one variable. One popular example is solving for (x) in equations like (3x + 5 = 2x + 12). Whether you're a student learning algebra or simply looking to sharpen your problem-solving skills, this guide will walk you through step-by-step how to solve (3x + 5 = 2x + 12), why it works, and how it applies broadly to simplifying real-world problems.", "### What Does It Mean to Solve for (x)?", "In algebra, solving for (x) means finding the value of (x) that makes the equation true. In the equation:\n[ 3x + 5 = 2x + 12 ]\nwe want to determine the exact value of (x) that balances both sides of the equation.", "### Step-by-Step Solution", "Step 1: Isolate the variable terms on one side\nTo solve for (x), begin by getting all terms containing (x) on one side of the equation. Subtract (2x) from both sides:\n[\n3x + 5 - 2x = 2x + 12 - 2x\n]\nThis simplifies to:\n[\nx + 5 = 12\n]", "Step 2: Eliminate constant terms\nNow subtract 5 from both sides to isolate (x):\n[\nx + 5 - 5 = 12 - 5\n]\nThis simplifies to:\n[\nx = 7\n]", "### Verifying the Solution", "It’s always a good practice to substitute your solution back into the original equation to ensure correctness:\nLeft side: (3x + 5 = 3(7) + 5 = 21 + 5 = 26)\nRight side: (2x + 12 = 2(7) + 12 = 14 + 12 = 26)\nSince both sides are equal, (x = 7) satisfies the equation.", "### Why Solving Linear Equations Like This Is Important", "Equations such as (3x + 5 = 2x + 12) appear frequently in everyday contexts—from budgeting and fixing salaries, to planning materials in architecture or engineering. Understanding how to isolate (x) helps build logical reasoning and analytical skills essential in science, finance, and technology fields.", "### Summary", "- Start by isolating variable terms on one side.\n- Remove constants to leave the variable standalone.\n- Verify the solution by plugging it back into the original equation.\n- Practice makes perfect—this pattern applies across countless real-life equations.", "Mastering how to solve for (x) in equations like (3x + 5 = 2x + 12) sets a strong foundation for advanced mathematics and problem-solving across disciplines.", "---", "Keywords for SEO:\nSolve for (x), linear equations, algebraic equation solving, step-by-step math tutorial, how to solve (3x + 5 = 2x + 12), algebra practice, real-world math applications, math problem solving.", "Meta Description:\nLearn how to solve for (x) in the equation (3x + 5 = 2x + 12) with step-by-step instructions, verification tips, and real-world relevance. Perfect for students and math enthusiasts."]