The ratio is \( 3/2 = 15/x \).
["Understanding the Equation: Solving ( \frac{3}{2} = \frac{15}{x} )", "When faced with the equation ( \frac{3}{2} = \frac{15}{x} ), many people wonder how to solve for ( x )—a common algebraic problem that also brings clarity on proportional reasoning. This ratio-based equation is a great example of how fractions and algebra work together to find unknown values.", "### What Does the Equation Mean?", "The equation ( \frac{3}{2} = \frac{15}{x} ) expresses that the ratio of 3 to 2 is equivalent to the ratio of 15 to ( x ). In practical terms, this might represent rates, proportions, or scaling factors—common scenarios in math, science, and real-world problem-solving.", "---", "### Step-by-Step Solution", "To solve for ( x ), follow these algebraic steps:", "1. Set up the equation:\n [\n \frac{3}{2} = \frac{15}{x}\n ]", "2. Cross-multiply to eliminate fractions:\n [\n 3 \cdot x = 2 \cdot 15\n ]\n [\n 3x = 30\n ]", "3. Divide both sides by 3:\n [\n x = \frac{30}{3} = 10\n ]", "---", "### The Solution", "The value of ( x ) satisfying the equation ( \frac{3}{2} = \frac{15}{x} ) is:", "[\n\boxed{x = 10}\n]", "---", "### Why This Ratio Matters", "Understanding how to manipulate ratios like ( \frac{3}{2} = \frac{15}{x} ) helps in many fields:", "- Proportional reasoning underpins tasks such as converting units, scaling recipes, or adjusting designs.\n- Algebraic problem-solving skills developed here apply to complex equations in higher mathematics.\n- Proportion equations frequently model real-world phenomena like speed, density, and density-based calculations.", "---", "### How to Solve Ratio Problems Like This", "- Cross-multiply—this turns the ratio idea into a solvable equation.\n- Isolate the unknown variable and use inverse operations (multiply or divide) to solve.\n- Check your answer by plugging ( x = 10 ) back into the original ratio:\n [\n \frac{3}{2} = \frac{15}{10} = 1.5 \quad \ ext{which is } 1.5 = 1.5 \quad \ ext{✓ confirmation}\n ]", "---", "### Summary", "The equation ( \frac{3}{2} = \frac{15}{x} ) illustrates a classic ratio comparison solvable through cross-multiplication. With the solution ( x = 10 ), this problem demonstrates how algebraic techniques unlock unknowns in proportional relationships—foundations for deeper mathematical thinking.", "Never underestimate the power of ratios and proportions—they’re essential tools in learning, teaching, and everyday logic.", "---", "Keywords: ratio equation, solve ( \frac{3}{2} = \frac{15}{x} ), algebraic proportions, fractional equation, math problem solution, cross multiplication, solving for ( x ), proportional reasoning."]
