Multiply both sides by 3: \( 2x - 1 = 15 \)

["How to Multiply Both Sides by 3: Solving the Equation ( 2x - 1 = 15 )", "Want to solve the equation ( 2x - 1 = 15 ) and make number manipulation easier? One common and effective step is multiplying both sides by 3. This simple technique helps eliminate fraction coefficients or prepare the equation for the next step, especially when isolating the variable. In this article, we’ll walk through how to multiply both sides by 3, solve the equation step by step, and explore why this multiplication is a useful strategy in algebra.", "---", "### Understanding the Equation", "We begin with:\n[\n2x - 1 = 15\n]\nOur goal is to solve for ( x )—that is, find the value that makes the equation true. Right now, the term ( 2x ) means we need to isolate ( x ), but there’s also a constant term (-1) that needs to be removed.", "---", "### Multiplying Both Sides by 3", "Multiplying both sides by 3 simplifies the expression and clears the constant:\n[\n3 \ imes (2x - 1) = 3 \ imes 15\n]", "Apply the distributive property on the left side:\n[\n3 \cdot 2x - 3 \cdot 1 = 45\n]\n[\n6x - 3 = 45\n]", "Now the equation looks cleaner and removes the fraction that would otherwise complicate solving.", "---", "### Isolating the Variable", "Next, add 3 to both sides to isolate the term with ( x ):\n[\n6x - 3 + 3 = 45 + 3\n]\n[\n6x = 48\n]", "Now divide both sides by 6:\n[\nx = \frac{48}{6} = 8\n]", "---", "### Verifying the Solution", "Plug ( x = 8 ) back into the original equation:\n[\n2(8) - 1 = 16 - 1 = 15\n]\nIt checks out! The left side equals the right side.", "---", "### Why Multiply by 3?", "Multiplying both sides by 3 simplifies solving by:\n- Removing subtraction in ( 2x - 1 ), making it easier to isolate ( x ).\n- Avoiding fractions if one later wants to divide by 6 (as in ( 6x = 48 )).\n- Enforcing standard form closer to ( x = \ ext{something} ), a common target in algebra.", "This step accelerates problem-solving without altering the solution’s integrity—just reframing the equation for clarity.", "---", "### Final Answer", "[\nx = 8\n]", "---", "### Key Takeaways", "- Multiply both sides by a common factor (here, 3) to simplify coefficients.\n- Always apply the same operation to both sides to maintain equation balance.\n- Use multiplication to eliminate constants and reduce complexity.\n- Verify your solution by substituting back into the original equation.", "---", "Mastering this step gives you a solid foundation for solving linear equations efficiently. Whether you're learning algebra or reviewing concepts, remembering to clear constants by multiplying sets you up for smoother problem-solving ahead."]