Simplify: \(40 + 0.7x = 50 + 0.5x\).
["# Simplify: (40 + 0.7x = 50 + 0.5x)\nStep-by-Step Algebra Simplification & Solution", "Equation-solving is a fundamental skill in algebra, helping students and math enthusiasts alike to isolate variables and uncover unknown values. In this article, we’ll simplify and solve the linear equation (40 + 0.7x = 50 + 0.5x), explaining each step clearly to enhance understanding and confidence in handling similar equations. Whether you're a high school student or a lifelong learner, mastering this method strengthens your algebraic foundation.", "## The Equation at a Glance", "We begin with the equation:", "[\n40 + 0.7x = 50 + 0.5x\n]", "Our goal is to isolate (x) by simplifying both sides through algebraic manipulation.", "## Step 1: Eliminate the variable terms on one side", "Our strategy is to move all terms containing (x) to one side of the equation and constant terms to the opposite side. Here, (0.7x) and (0.5x) are the variable terms, while 40 and 50 are constants. Subtract (0.5x) from both sides:", "[\n40 + 0.7x - 0.5x = 50 + 0.5x - 0.5x\n]", "Simplify both sides:", "[\n40 + 0.2x = 50\n]", "## Step 2: Move constants to the opposite side", "Now subtract 40 from both sides to isolate the term with (x):", "[\n40 + 0.2x - 40 = 50 - 40\n]", "Simplify:", "[\n0.2x = 10\n]", "## Step 3: Solve for (x)", "To find (x), divide both sides by 0.2 (or multiply by 5):", "[\nx = \frac{10}{0.2} = 50\n]", "## Final Result", "[\n\boxed{x = 50}\n]", "## Why This Method Works", "By systematically eliminating like terms and isolating the variable, we transform a complex equation into a simple linear form (ax = b), where solving becomes straightforward. This approach fosters logical thinking and precision, essential for mastering algebra.", "## Practice Makes Perfect", "Want to try more? Try simplifying other equations like (12 + 0.3x = 18 + 0.4x) using the same method. With practice, simplifying linear equations becomes quick and intuitive.", "---", "Keywords: simplify linear equation, solve 0.7x = 0.5x, algebraic steps, equation solving tip, algebra help, step-by-step math, how to solve equations\nMeta Description: Learn how to simplify and solve (40 + 0.7x = 50 + 0.5x) step-by-step with full explanation—perfect for mastering basic algebra."]
