Simplifying: \( 155 = 5 (10 + 9d) \) → \( 155 = 50 + 45d \) → \( 105 = 45d \) → \( d = \frac{105}{45} = \frac{7}{3} \).
["How to Simplify the Equation ( 155 = 5(10 + 9d) ) Step-by-Step", "Solving equations step-by-step can make complex algebra easier to understand. In this guide, we’ll simplify the equation ( 155 = 5(10 + 9d) ) into its final solution: ( d = \frac{7}{3} ), using clear, logical steps.", "---", "### Step 1: Eliminate the Parentheses\nStart by expanding the right-hand side using the distributive property:\n[ 155 = 5(10 + 9d) ]\nMultiply 5 by both terms inside the parentheses:\n[ 155 = 5 \ imes 10 + 5 \ imes 9d ]\n[ 155 = 50 + 45d ]", "---", "### Step 2: Isolate the Term With ( d )\nSubtract 50 from both sides to isolate the term containing ( d ):\n[ 155 - 50 = 45d ]\n[ 105 = 45d ]", "---", "### Step 3: Solve for ( d )\nDivide both sides by 45 to solve for ( d ):\n[ d = \frac{105}{45} ]", "Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 15:\n[ d = \frac{105 \div 15}{45 \div 15} = \frac{7}{3} ]", "---", "### Final Answer\nThe simplified solution is:\n[ \boxed{d = \frac{7}{3}} ]", "Simplifying equations step-by-step not only confirms correctness but also builds confidence in handling algebraic expressions. Understanding how distributive properties and basic algebra manipulate expressions helps streamline problem-solving for better mastery of math concepts.", "---", "Keywords: simplify algebra, solving linear equations, step-by-step solving, algebraic simplification, equation solving, fraction simplification, ( 155 = 5(10 + 9d) ), ( d = \frac{7}{3} )"]
