\(3 = 1.5 + 0.10x\).

["# How to Solve (3 = 1.5 + 0.10x): A Step-by-Step Guide", "Understanding how to solve linear equations like (3 = 1.5 + 0.10x) is essential for anyone learning basic algebra. Whether you're a high school student, a self-learner, or someone needing a refresher, this article walks you through the process clearly and methodically. Mastering these skills helps build a strong foundation for more advanced math topics and real-world problem-solving.", "---", "## What Is the Equation (3 = 1.5 + 0.10x)?", "The equation (3 = 1.5 + 0.10x) is a simple linear equation involving a constant term (1.5), a coefficient (0.10), and a variable (x). Solving it means finding the value of (x) that makes the equation true. This type of equation is common in everyday applications, from budgeting and fitness tracking to finance and science.", "---", "## Why Solving Linear Equations Matters", "Linear equations form the backbone of algebra. They teach critical thinking and logical reasoning. Beyond homework, knowing how to isolate variables helps in interpreting graphs, analyzing trends, and making predictions. Mastering basic forms like (3 = 1.5 + 0.10x) prepares you for more complex equations and higher-level math.", "---", "## Step-by-Step Solution", "We’ll solve (3 = 1.5 + 0.10x) using fundamental algebraic principles. Here’s how:", "### Step 1: Identify the Variable", "Our goal is to isolate (x). The variable appears on one side (the unknown) and is multiplied by 0.10.", "### Step 2: Subtract the Constant", "To begin isolating (x), remove constant terms from the side containing (x). Subtract 1.5 from both sides:", "[\n3 - 1.5 = 1.5 + 0.10x - 1.5\n]", "Simplify:", "[\n1.5 = 0.10x\n]", "### Step 3: Divide to Isolate (x)", "Now divide both sides by 0.10 to solve for (x):", "[\nx = \frac{1.5}{0.10}\n]", "Calculate:", "[\nx = 15\n]", "---", "## Verification", "Plug (x = 15) back into the original equation to confirm:", "[\n3 = 1.5 + 0.10(15)\n]", "[\n3 = 1.5 + 1.5\n]", "[\n3 = 3 \quad \ ext{(True)}\n]", "The solution checks out!", "---", "## Real-World Applications", "Equation (3 = 1.5 + 0.10x) might model practical situations:", "- Budgeting: Suppose you earn $0.10 per task completed, with a fixed $1.50 daily income. To earn a total of $3 per day, how many tasks must you complete?\n- Fitness: You start with 1.5 lbs of weight to lose, aiming total loss of 3 lbs using a daily program increasing loss by 0.10 lbs per session. How many sessions?", "---", "## Tips to Solve Linear Equations Quickly", "- Always keep operations balanced on both sides of the equation.\n- Simplify constants before isolating the variable.\n- Use inverse operations systematically: subtraction/addition before multiplication/division.\n- Always check your solution by substituting back.", "---", "## Summary", "Solving (3 = 1.5 + 0.10x) involves isolating (x) by first reducing constants, then dividing. The solution, (x = 15), validates the balance of the equation. This core skill advances your algebra proficiency and empowers you to tackle real-world quantitative challenges.", "---", "Keywords:\nsolve linear equation (3 = 1.5 + 0.10x), algebraic equation solving, linear equations tutorial, step-by-step math, elementary algebra, how to solve for x, real-world math applications, practice equation solving", "---", "Mastering equations like (3 = 1.5 + 0.10x) unlocks new math territory—keep practicing, and watch your confidence and capability grow!"]