x + 0.25x = $75.

["Solve for x: How to Solve x + 0.25x = 75 (Step-by-Step Guide)", "Ever come across the equation x + 0.25x = 75 and wondered how to solve it? Whether you're a student learning algebra or someone simply trying to understand basic financial math, knowing how to solve linear equations like this is essential. In this article, we’ll break down step-by-step how to solve for x in the equation x + 0.25x = 75, explain its real-world applications, and highlight its relevance in everyday math and finance.", "---", "### Understanding the Equation: What Does x + 0.25x = 75 Mean?", "The expression x + 0.25x = 75 involves combining like terms and solving for the variable x. Here, x represents an unknown quantity, while 0.25x is a quarter of x. This kind of expression often appears in budgeting, profit calculations, and financial planning.", "---", "### Step 1: Combine Like Terms", "To begin solving x + 0.25x = 75, combine the x terms on the left-hand side:", "[\nx + 0.25x = (1 + 0.25)x = 1.25x\n]", "So, the equation simplifies to:", "[\n1.25x = 75\n]", "---", "### Step 2: Isolate the Variable x", "Now divide both sides of the equation by 1.25 to isolate x:", "[\nx = \frac{75}{1.25}\n]", "Performing the division:", "[\nx = 60\n]", "---", "### Step 3: Check Your Answer", "To confirm, substitute x = 60 back into the original equation:", "[\n60 + 0.25(60) = 60 + 15 = 75\n]", "✔️ The equation holds true — the solution is correct.", "---", "### Why This Equation Matters: Real-World Applications", "Solving equations like x + 0.25x = 75 is more than just textbook math. In personal finance, for example, this format might represent a budget where x is your base income, and 0.25x is a percentage set aside for savings or expenses. Understanding how to manipulate such equations helps you calculate exact figures, balance budgets, or forecast earnings.", "---", "### Bonus: Using This Formula in Other Contexts", "- Business: Calculate the base revenue needed when profits include variable contributions (e.g., x sales + 25% of sales = $75 net).\n- Economics: Determine base prices when combined with markups or deductions.\n- School Math: This equation reinforces foundational algebraic skills used in high-school math and standardized tests.", "---", "### Summary", "Solving x + 0.25x = 75 involves:\n1. Combining like terms: 1.25x\n2. Dividing both sides by 1.25\n3. Verifying the solution\n4. Understanding its use in budgeting, finance, and problem-solving", "The answer is x = 60, meaning the unknown value equals $60 in this context.", "---", "Key Takeaway: Mastering simple linear equations like x + 0.25x = 75 empowers you to tackle real-life math challenges confidently. Whether budgeting, calculating profits, or interpreting financial data, knowing how to manipulate and solve equations is a powerful skill.", "---", "Feel free to explore related topics:\n- How to solve linear equations step-by-step\n- Applications of algebra in personal finance\n- Tips for improving your math skills for tests and real life", "Search terms for further reading:\nhow to solve x + 0.25x = 75\nstep-by-step linear equation tutorial\nx + 0.25x = 75 real-life examples\nbenefits of algebra in financial planning"]