\Rightarrow 0.15x + 4 - 0.40x = 2.5

["Solving the Linear Equation: Step-by-Step Guide to ← 0.15x + 4 − 0.40x = 2.5", "Understanding how to solve linear equations is essential in algebra and forms the foundation for more advanced math topics. One common exercise students encounter is solving equations like −0.40x + 0.15x + 4 = 2.5, which simplifies neatly but requires a careful step-by-step approach. In this article, we’ll break down the process of solving the equation ← 0.15x + 4 − 0.40x = 2.5, explain why simplification matters, and provide practical guidance to solve similar linear equations efficiently.", "---", "### What Is the Equation?", "The equation in focus is:\n−0.40x + 0.15x + 4 = 2.5", "This linear equation features coefficients representing x, a constant term, and a right-hand side constant. The goal is to isolate x and find its value.", "---", "### Step 1: Combine Like Terms", "To solve the equation, begin by combining like terms on the left-hand side. Specifically, combine the coefficients of x:", "[\n(-0.40x + 0.15x) + 4 = 2.5\n]", "[\n(-0.25x) + 4 = 2.5\n]", "Explanation:\n- Add the coefficients: (-0.40 + 0.15 = -0.25), so we simplify to (-0.25x + 4 = 2.5).", "---", "### Step 2: Isolate the Variable Term", "Next, subtract 4 from both sides to move the constant to the right:", "[\n-0.25x + 4 - 4 = 2.5 - 4\n]", "[\n-0.25x = -1.5\n]", "Explanation:\n- Subtracting 4 removes it from the left side.\n- Simplify right-hand side: (2.5 - 4 = -1.5).", "---", "### Step 3: Solve for x", "Now divide both sides by (-0.25) to isolate x:", "[\nx = \frac{-1.5}{-0.25}\n]", "[\nx = 6\n]", "Explanation:\n- Since both numerator and denominator are negative, the negatives cancel, giving a positive result.\n- Divide: (1.5 ÷ 0.25 = 6) (since (0.25 = \frac{1}{4}), dividing by 0.25 is equivalent to multiplying by 4).", "---", "### Final Answer", "[\n\boxed{x = 6}\n]", "---", "### Why Solving Linear Equations Like This Matters", "Linear equations such as −0.40x + 0.15x + 4 = 2.5 appear in real-life scenarios ranging from budgeting and physics to business modeling and computer science. Mastering their solution helps strengthen problem-solving skills, enhances logical thinking, and prepares learners for higher-level math, including systems of equations and linear programming.", "---", "### Practice Problems & Tips", "To become fluent in solving equations like this, try these:", "- Combine like terms first.\n- Always isolate the variable step by step.\n- Remember to keep signs consistent—negative divided by negative yields positive.\n- Check your solution by plugging (x = 6) back into the original equation.", "[\n-0.40(6) + 0.15(6) + 4 = -2.4 + 0.9 + 4 = 2.5 \quad \ ext{(Correct!)}\n]", "---", "### Conclusion", "Solving 0.15x + 4 − 0.40x = 2.5 simplifies to (-0.25x + 4 = 2.5), then to (x = 6). By following systematic steps—combining like terms, isolating variables, and simplifying—any linear equation becomes manageable. Keep practising these foundational skills, and soon algebra will feel like second nature!", "---", "Keywords for SEO:\nlinear equation solution, how to solve -0.40x + 0.15x + 4 = 2.5, step-by-step algebra, solve linear equations, simplify algebraic expressions, real world math examples, algebraic manipulation tips", "Meta Description:\nLearn how to solve −0.40x + 0.15x + 4 = 2.5 step by step. Understand combining like terms, isolating variables, and verifying solutions. Perfect for students mastering algebra."]