Solve for \( x \): \( \frac{2x - 1}{3} = 5 \)

["Solve for ( x ): ( \frac{2x - 1}{3} = 5 )", "Solving equations is a fundamental skill in algebra, and understanding how to isolate the variable is essential for further math studies and real-world applications. In this article, we’ll walk step-by-step through solving the equation:", "[\n\frac{2x - 1}{3} = 5\n]", "---", "### Step 1: Eliminate the Denominator", "To simplify the equation, we start by removing the denominator. Since the left side is divided by 3, multiply both sides of the equation by 3:", "[\n3 \cdot \frac{2x - 1}{3} = 3 \cdot 5\n]", "Simplifying both sides gives:", "[\n2x - 1 = 15\n]", "---", "### Step 2: Isolate the Variable Term", "Next, isolate the term containing ( x ) by adding 1 to both sides:", "[\n2x - 1 + 1 = 15 + 1\n]", "This simplifies to:", "[\n2x = 16\n]", "---", "### Step 3: Solve for ( x )", "Finally, divide both sides by 2 to solve for ( x ):", "[\nx = \frac{16}{2} = 8\n]", "---", "### Final Answer", "[\nx = 8\n]", "---", "### Summary", "Solving ( \frac{2x - 1}{3} = 5 ) involves clearing the fraction, isolating the variable expression, and performing inverse operations step-by-step. By following these algebra fundamentals, you build strong calculation habits useful in advanced mathematics, science, engineering, and everyday problem solving.", "Key Takeaways:\n- Multiply both sides by denominator to eliminate fractions.\n- Use addition to isolate the term with ( x ).\n- Apply division to find the final solution.", "---", "### Practice: Try solving this extension:", "[\n\frac{3x + 2}{4} = 7\n]", "Follow the same steps and verify your answer!", "---", "Optimizing this content with relevant keywords like "[solve linear equation", "algebraic equation steps", and "solve for x", helps improve SEO while guiding new learners through a fundamental algebraic concept."]