Solving for \(x\), \(3 = 0.10(15 + x)\).
["# Solving for ( x ) in the Equation ( 3 = 0.10(15 + x) )", "Solving linear equations is a fundamental skill in algebra, essential for beginners and a key step in tackling more complex mathematical problems. One common equation students encounter is ( 3 = 0.10(15 + x) ). Whether you're a student preparing for exams, a teacher guiding students, or someone brushing up on math fundamentals, understanding how to solve for ( x ) in this equation can boost your confidence and clarity in algebra.", "## Understanding the Equation", "The original equation is:", "[\n3 = 0.10(15 + x)\n]", "This expression involves multiplication and a real-world application—often used in financial contexts like calculating payments or interest. Our goal is to isolate the variable ( x ) and determine its value.", "## Step-by-Step Solution", "### Step 1: Distribute the coefficient", "Start by eliminating the parentheses using the distributive property:", "[\n3 = 0.10 \ imes 15 + 0.10x\n]", "Calculate ( 0.10 \ imes 15 ):", "[\n3 = 1.5 + 0.10x\n]", "### Step 2: Isolate the term with ( x )", "Subtract 1.5 from both sides to move the constant term to the left:", "[\n3 - 1.5 = 0.10x\n]", "[\n1.5 = 0.10x\n]", "### Step 3: Solve for ( x )", "To isolate ( x ), divide both sides by 0.10:", "[\nx = \frac{1.5}{0.10}\n]", "[\nx = 15\n]", "## Final Answer", "[\n\boxed{15}\n]", "So, when solving ( 3 = 0.10(15 + x) ), the solution is ( x = 15 ). This means that when ( x = 15 ), the expression ( 0.10(15 + x) ) evaluates exactly to 3.", "## Why This Equation Matters", "This problem demonstrates how linear equations model relationships involving scaling and fixed quantities. In real life, such equations can represent everything from budgeting scenarios—where $0.10 per unit applies over a base cost of $15—making it a practical and illustrative example.", "## Tips for Practicing", "- Always start by simplifying parentheses using the distributive property.\n- Keep track of units—especially decimals—to avoid arithmetic errors.\n- Always isolate the variable step by step before performing division.", "Mastering this simple equation strengthens your foundation in algebraic reasoning, preparing you for advanced topics like systems of equations and linear modeling.", "---", "If you're looking to deepen your understanding, practice solving similar equations involving percentages, fixed costs, or variable terms. Consistent practice leads to fluency and greater confidence in math!"]
