0.25x + 30 - 0.10x = 45

["# How to Solve: 0.25x + 30 - 0.10x = 45 – A Step-by-Step Guide", "Understanding how to solve linear equations like 0.25x + 30 - 0.10x = 45 is essential for mastering algebra. Whether you're a student, educator, or problem-solver, breaking down this equation step-by-step can clarify how to isolate variables and find accurate solutions. In this article, we’ll explain how to solve 0.25x + 30 - 0.10x = 45 clearly, why each step matters, and how this process applies to real-life math problems.", "## Understanding the Equation", "The equation 0.25x + 30 - 0.10x = 45 is a linear equation in one variable, x. Linear equations involve variables raised to the first power and can be simplified algebraically to isolate x. Solving equations like this is foundational for higher mathematics, science, and engineering applications.", "## Step 1: Combine Like Terms", "The left side of the equation includes two variables with the same base: 0.25x – 0.10x. Simplify these terms by combining coefficients:", "[\n0.25x - 0.10x = (0.25 - 0.10)x = 0.15x\n]", "Now rewrite the equation:", "[\n0.15x + 30 = 45\n]", "Combining constants helps streamline the solving process, focusing on isolating x.", "## Step 2: Isolate the Variable Term", "To isolate 0.15x, subtract 30 from both sides of the equation:", "[\n0.15x + 30 - 30 = 45 - 30\n]\n[\n0.15x = 15\n]", "This step removes the constant term from the left side, leaving just the coefficient multiplied by x.", "## Step 3: Solve for x", "Now divide both sides by 0.15 to solve for x:", "[\nx = \frac{15}{0.15}\n]", "Simplify the division:", "[\nx = 100\n]", "## Why This Works", "Each step follows algebraic principles: combining like terms reduces complexity, subtracting constants isolates the variable term, and division removes the coefficient. This method ensures precision and avoids common errors in equation solving.", "## Example Verification", "Plug x = 100 back into the original equation:", "[\n0.25(100) + 30 - 0.10(100) = 25 + 30 - 10 = 45\n]", "The left side equals the right side, confirming x = 100 is correct.", "## Real-World Applications", "Problems like 0.25x + 30 - 0.10x = 45 often appear in financial modeling (e.g., profit calculations with variable costs), science (balancing chemical equations numerically), and daily budgeting where Net values depend on fixed and variable amounts.", "## Conclusion", "Solving 0.25x + 30 - 0.10x = 45 follows a clear, logical sequence: combine like terms, isolate the variable, and solve. This approach not only answers the equation accurately but also strengthens core algebraic reasoning. Practice these steps regularly to build confidence and fluency in algebra — a critical skill across academic and professional fields.", "---", "Keywords for SEO: solve 0.25x + 30 - 0.10x = 45, linear equation algebra, how to solve variable equations, step-by-step solving x, equation solving with decimals, real-world math problem, algebra practice problems.", "---", "Learn more about algebraic techniques and solving strategies at your favorite educational platform or math resource!"]