["# Simplify (3x - 2 = 2x + 10): Step-by-Step Solution for Beginners", "If you've ever felt stuck when solving a linear equation like (3x - 2 = 2x + 10), don’t worry—you’re not alone! In this beginner-friendly guide, we’ll walk through how to simplify and solve this equation step by step, making it easy to master solving one variable equations. Whether you're a student tackling algebra for the first time or just looking to refresh your skills, simplifying (3x - 2 = 2x + 10) will build confidence in basic algebra.", "---", "## What Equation Are We Solving?", "The equation we want to simplify and solve is:
\n[ 3x - 2 = 2x + 10 ]", "This is a linear equation because it involves only one variable (x) and the variable appears to the first power—no exponents or complex expressions. Our goal is to isolate (x) on one side and find its value.", "---", "## Step-by-Step Simplification and Solution", "### Step 1: Reduce both sides to get like terms together", "Our goal is to gather all terms containing (x) on one side and constant terms on the other.", "Start with:
\n[ 3x - 2 = 2x + 10 ]", "🔹 Subtract (2x) from both sides to move all (x) terms left:
\n[ 3x - 2 - 2x = 2x + 10 - 2x ]
\n[ x - 2 = 10 ]", "Now, constants are on the right side.", "---", "### Step 2: Eliminate constants to isolate (x)", "Add 2 to both sides to remove $-2) from the left:
\n[ x - 2 + 2 = 10 + 2 ]
\n[ x = 12 ]", "---", "## Final Answer", "After simplifying step by step, we find:
\n[ \boxed{x = 12} ]", "---", "## Why This Matters: Key Concepts Simplified", "- Moving terms: We move (2x) to the left by subtraction—remember, subtracting (2x) is the same as adding (-2x).
\n- Moving constants: Adding 2 to both sides keeps the equation balanced (balancing acts = equality maintained).
\n- Isolating (x): Subtracting 2 from both sides gives (x) by itself, revealing its value.", "---", "## Summary: How to Simplify (3x - 2 = 2x + 10)", "1. Identify like terms and variables.
\n2. Move variables to one side by subtracting or adding on both sides.
\n3. Shift constants to the opposite side with opposite sign operations.
\n4. Combine and isolate the variable.
\n5. Solve for (x).", "---", "## Practice Tips", "- Try similar equations like (4x + 5 = x - 3) or (7 - 2x = 3x + 1).
\n- Always perform the same operation on both sides.
\n- Check your answer by plugging (x = 12) back into the original equation:
\n Left: (3(12) - 2 = 36 - 2 = 34)
\n Right: (2(12) + 10 = 24 + 10 = 34)
\n ✅ Both sides equal—solution is correct!", "---", "## Related SEO Keywords", "- solve linear equations step by step
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\n- step-by-step equation solving guide", "---", "Mastering equations like (3x - 2 = 2x + 10) unlocks algebraic fluency. With practice, simplifying such expressions becomes quick and intuitive—so grab your pencil and try a few problems today!"]
