\(1.5 = 0.10x\).

["# Solve (1.5 = 0.10x): Step-by-Step Explanation", "Solving equations like (1.5 = 0.10x) is a fundamental skill in algebra that appears frequently in everyday math problems, science applications, and real-world scenarios such as budgeting, physics, and recipe scaling. In this article, we’ll walk through how to solve (1.5 = 0.10x) step-by-step, explain why this works, and show you practical ways to use this type of equation.", "---", "## Understanding the Equation: (1.5 = 0.10x)", "The equation (1.5 = 0.10x) is a linear equation where (x) represents an unknown value. It means that 0.10 multiplied by (x) equals 1.5. This format is common in many practical problems such as:", "- Calculating cost per unit when buying in bulk\n- Converting units with a fixed rate\n- Determining quantities in proportional relationships", "---", "## Step-by-Step Solution", "To solve for (x), follow these clear steps:", "### Step 1: Isolate the variable term\nThe goal is to get (x) by itself on one side of the equation. Currently, (x) is multiplied by 0.10:", "[\n1.5 = 0.10x\n]", "### Step 2: Divide both sides by 0.10\nTo isolate (x), divide both sides of the equation by 0.10:", "[\nx = \frac{1.5}{0.10}\n]", "### Step 3: Perform the division\nNow compute:", "[\nx = \frac{1.5}{0.10} = 15\n]", "---", "## Final Answer", "[\n\boxed{x = 15}\n]", "This means the solution to (1.5 = 0.10x) is (x = 15).", "---", "## Why This Works: The Math Behind It", "When you divide both sides of the equation by the coefficient of (x) (here, 0.10), you effectively undo multiplication. This rule is based on the inverse operation principle in algebra:", "[\n\ ext{If } a = b \ imes c,\ \ ext{then } x = \frac{a}{c}\n]", "By dividing both sides by (0.10), we keep the equation balanced while solving for (x).", "---", "## Real-World Applications of Solving Linear Equations Like This", "### 1. Price and Quantity Calculations\nSuppose you pay $1.50 for 0.10 units of a product. To find the price per unit, divide total cost by quantity:\n[\n\ ext{Price per unit} = \frac{1.50}{0.10} = 15~\ ext{dollars per unit}\n]", "### 2. Scaling Recipes\nIf a recipe serves 2 people and costs $1.50, how much does it cost to serve 15 people?\nSince (x = 15) is your scaling factor, you multiply total cost by 15, but knowing the per-person cost helps budget.", "### 3. Distance and Speed Problems\nIn unit conversions or basic physics, similar equations describe relationships like distance = speed × time — solving for unknowns often involves division.", "---", "## Practice Problems to Reinforce Learning", "1. Solve: (2.4 = 0.06x)\n2. If $5.10 is spent at $0.15 per unit, how many units bought? ((x = ?))\n3. A 1.2-meter rope is cut into pieces each (0.1) meters long. How many pieces?", "---", "## Summary", "- The equation (1.5 = 0.10x) has solution (x = 15).\n- Solving linear equations involves isolating the variable using inverse operations.\n- This type of equation applies widely in budgeting, science, and daily calculations.\n- Always maintain balance on both sides of the equation.", "Mastering these steps empowers you to tackle similar math challenges confidently, whether in school, work, or real life.", "---", "Keywords: solve (1.5 = 0.10x), algebra basics, linear equation, divide by 0.10, math tutorial, real world problems, step-by-step algebra, ratio and proportion, practical math equations."]