Solve for \( x \) in the equation \( 3x + 4 = 2x + 10 \).
["# Solving for ( x ) in the Equation ( 3x + 4 = 2x + 10 )", "Solving simple linear equations is a foundational skill in algebra, and one of the most common problems students encounter is isolating the variable ( x ). A typical example is the equation:\n[ 3x + 4 = 2x + 10 ]", "In this article, we’ll walk through the step-by-step process of solving for ( x ), explain why each step works, and highlight why mastering this technique matters in math and real-world applications.", "---", "## What Does It Mean to Solve for ( x )?", "When we solve an equation like ( 3x + 4 = 2x + 10 ), we aim to find the value of the unknown variable ( x ) that makes both sides of the equation equal. This process isolates ( x ) on one side, transforming the equation into a clear statement:\n[ x = \ ext{(some number)} ]", "---", "## Step-by-Step Solution", "### Step 1: Eliminate ( x ) Terms from One Side", "To isolate ( x ), begin by removing ( 2x ) from the right side. Subtract ( 2x ) from both sides to maintain equality:\n[ 3x + 4 - 2x = 2x + 10 - 2x ]\n[ (3x - 2x) + 4 = 10 ]\n[ x + 4 = 10 ]", "Now, the equation simplifies to:\n[ x + 4 = 10 ]", "### Step 2: Remove the Constant Term", "Next, subtract ( 4 ) from both sides to eliminate the constant term on the left:\n[ x + 4 - 4 = 10 - 4 ]\n[ x = 6 ]", "---", "## Final Answer", "The solution to the equation ( 3x + 4 = 2x + 10 ) is:\n[ x = 6 ]", "Verifying this result: Substitute ( x = 6 ) back into the original equation:\n[ 3(6) + 4 = 2(6) + 10 ]\n[ 18 + 4 = 12 + 10 ]\n[ 22 = 22 ]", "Since both sides are equal, our solution is correct.", "---", "## Why Learning to Solve Linear Equations Matters", "Mastering equations like ( 3x + 4 = 2x + 10 ) isn’t just about algebra—it’s about developing problem-solving skills essential in science, engineering, finance, and everyday decision-making. These skills help you:\n- Deduce unknown values from known data.\n- Model real-world situations mathematically.\n- Build a stronger foundation for advanced topics like quadratic equations and calculus.", "---", "## Conclusion", "Solving ( 3x + 4 = 2x + 10 ) involves simple but critical steps: eliminating variables and isolating the unknown. With practice, this process becomes quick and intuitive, empowering learners to tackle more complex equations with confidence. Whether you’re analyzing data or coding algorithms, knowing how to solve for ( x ) is an indispensable skill.", "Start sharpening your algebraic skills today—your future self (and your next math test!) will thank you."]
