\[ 150 = 5 (10 + 9d) \]

["# How to Solve the Equation: 150 = 5(10 + 9d)", "Understanding how to solve linear equations like ( 150 = 5(10 + 9d) ) is a fundamental skill in algebra that empowers students and lifelong learners alike. This step-by-step guide will walk you through solving the equation, explain key algebraic concepts, and show how the solution supports broader problem-solving abilities.", "---", "## What is the Equation?", "The equation to solve is:", "[\n150 = 5(10 + 9d)\n]", "This is a linear equation in one variable, where ( d ) represents an unknown value we must determine.", "---", "## Step-by-Step Solution", "### Step 1: Distribute the 5 on the right side", "First, simplify the right-hand side by distributing the 5 across the parentheses:", "[\n150 = 5 \cdot 10 + 5 \cdot 9d\n]\n[\n150 = 50 + 45d\n]", "---", "### Step 2: Isolate the term containing ( d )", "Subtract 50 from both sides to move the constant to the left:", "[\n150 - 50 = 45d\n]\n[\n100 = 45d\n]", "---", "### Step 3: Solve for ( d )", "Divide both sides by 45 to isolate ( d ):", "[\nd = \frac{100}{45}\n]", "Simplify the fraction by dividing numerator and denominator by 5:", "[\nd = \frac{20}{9}\n]", "---", "## Final Answer", "[\n\boxed{ d = \frac{20}{9} }\n]", "This is the exact solution. As a decimal, ( d \approx 2.22 ), but the fraction form is preferred in algebraic contexts.", "---", "## Why This Equation Matters", "Solving equations like ( 150 = 5(10 + 9d) ) builds critical algebraic reasoning skills. These abilities are essential for:", "- Simplifying real-world problems\n- Managing variables in science and engineering\n- Advancing to more complex math topics such as systems of equations and functions", "---", "## Tips for Mastering Equation Solving", "1. Always isolate the variable term on one side—never both sides together.\n2. Use inverse operations: addition reverses subtraction, multiplication reverses division, etc.\n3. Check your solution by substituting back into the original equation.", "[\n150 = 5(10 + 9 \cdot \frac{20}{9}) = 5(10 + 20) = 5 \ imes 30 = 150 \quad \ ext{✓}\n]", "---", "## Conclusion", "Mastering linear equations such as ( 150 = 5(10 + 9d) ) strengthens your algebraic foundation and boosts confidence in tackling mathematical challenges. Practice recognizing patterns, simplifying expressions, and practicing solutions like this one to unlock deeper understanding.", "---", "### Key Search Terms (SEO Keywords)", "- Solve 150 = 5(10 + 9d)\n- Algebraic equation solving\n- Linear equation work steps\n- How to isolate variables\n- Step-by-step algebra practice\n- Equation solution tutorial", "---", "Learn, practice, and unlock algebraic mastery—one equation at a time!"]