Multiplying both sides by \(\frac{2}{3}\) gives:

["Multiplying Both Sides by (\frac{2}{3}): A Step-by-Step Guide for Students", "When solving equations, one of the fundamental skills is manipulating both sides to isolate the variable. A common instruction in algebra is: multiply both sides by (\frac{2}{3}). But what does this really mean, and how does multiplying by (\frac{2}{3}) help solve equations? This article explains clearly and introduces the core concept behind this operation using a straightforward example.", "---", "### What Does “Multiply Both Sides by (\frac{2}{3})” Mean?", "Multiplying both sides of an equation by (\frac{2}{3}) does not change the solution — it’s a valid operation that simplifies the equation. It leverages the properties of equality, specifically:", "> If (a = b), then (\frac{2}{3} \cdot a = \frac{2}{3} \cdot b)", "This is valid because multiplying both sides of an equality by the same non-zero number preserves the balance. This step often makes the equation easier to solve, especially when the coefficient of the variable is a fraction, such as (\frac{2}{3}).", "---", "### Why Multiply by (\frac{2}{3})?", "Consider a real-world or textbook scenario where you have an equation with (\frac{2}{3}) multiplied by the variable. For example:", "[\n\frac{2}{3}x = 4\n]", "To solve for (x), you want to isolate (x) by removing the fraction. Multiplying both sides by (\frac{3}{2}) (the reciprocal of (\frac{2}{3})) eliminates the fraction:", "[\n\frac{3}{2} \cdot \left( \frac{2}{3}x \right) = \frac{3}{2} \cdot 4\n]", "Simplifying both sides:", "- Left side: (\frac{3}{2} \cdot \frac{2}{3} x = 1 \cdot x = x)\n- Right side: (\frac{3}{2} \cdot 4 = 6)", "So the equation becomes:", "[\nx = 6\n]", "This technique turns a fraction into a clear whole, making it simpler to solve.", "---", "### When Is This Method Useful?", "- Fraction coefficients: When your variable is multiplied by a fraction, multiplying both sides by the fraction’s reciprocal removes the fraction and clears denominators.\n- Simplifying equations: It often reduces complexity, especially before applying other algebra steps like addition or distribution.\n- Preparing for inverse operations: Helping isolate (x) quickly and efficiently when dealing with fractional equations.", "---", "### Step-by-Step Summary", "1. Start with an equation involving a multiplication by (\frac{2}{3}), for example:\n [\n \frac{2}{3}x = 4\n ]\n2. Multiply both sides by (\frac{3}{2}):\n [\n \frac{3}{2} \cdot \left( \frac{2}{3}x \right) = \frac{3}{2} \cdot 4\n ]\n3. Simplify:\n [\n x = 6\n ]", "---", "### Final Thoughts", "Multiplying both sides of an equation by (\frac{2}{3}) is a strategic move in algebra that removes fractional coefficients and makes solving easier without altering the solution. By understanding its purpose and application, students gain confidence in manipulating equations—skills essential for success in higher-level math.", "Whether you’re a beginner or brushing up, remember: multiplying both sides by the reciprocal of a fraction is a powerful tool to simplify and solve equations efficiently.", "---", "Keywords: multiply both sides by (\frac{2}{3}), algebra tutorial, solving equations, fraction equations, reciprocal multiplication, solving for (x), equation simplification.\nMeta Description: Learn why multiplying both sides of an equation by (\frac{2}{3}) simplifies solving for (x). Step-by-step guide with real example and key math principles.\nHeader Tags: H1 — Multiplying Both Sides by (\frac{2}{3}): How to Solve Equations Step-by-Step\nH2: What Does Multiplying by (\frac{2}{3}) Mean in Equations?\nH3: Why Use (\frac{2}{3}) When Solving Linear Equations?\nH4: Practical Example: Solving (\frac{2}{3}x = 4)\nH2: Step-by-Step: Isolate (x) by Multiplying by (\frac{3}{2})\nH3: Quick Summary and Tips for Algebra Success", "---", "By integrating this concept with clear explanations, examples, and SEO-friendly structure, you create a valuable resource for learners seeking to master basic algebraic operations."]