Substituting known values: \( 155 = \frac{10}{2} (2 \times 5 + 9d) \).

["Title: Solving the Equation: ( 155 = \frac{10}{2}(2 \ imes 5 + 9d) ) – Step-by-Step Substitution Explained", "Meta Description:\nLearn how to solve the equation ( 155 = \frac{10}{2}(2 \ imes 5 + 9d) ) by systematically substituting known values. This guide simplifies algebra through clear step-by-step substitution methods.", "---", "### Introduction\nAlgebraic equations often require strategic substitution to simplify complex expressions. In this article, we’ll explore how to solve ( 155 = \frac{10}{2}(2 \ imes 5 + 9d) ) by carefully substituting known components—turning abstract expressions into real numbers step by step. Whether you're a student, educator, or curious learner, mastering substitution in equations helps build strong foundational math skills.", "---", "### Step 1: Understand the Structure of the Equation\nWe start with:\n[\n155 = \frac{10}{2}(2 \ imes 5 + 9d)\n]\nOur goal is to isolate ( d ). However, rather than solving directly from day one, we use substitution of inner values and sub-expressions to simplify and reduce clutter. Substituting known intervals early prevents compounding errors.", "---", "### Step 2: Substitute Simplest Numerical Constants\nBegin by identifying constants outside parentheses. Here, ( \frac{10}{2} = 5 ), a straightforward division:\n[\n155 = 5 \cdot (2 \ imes 5 + 9d)\n]\nAt this stage, the equation becomes clearer—we’ve substituted the scalar division, reducing the left side and eliminating parentheses temporarily.", "---", "### Step 3: Substitute and Simplify Inside Parentheses\nNow isolate the interior expression:\n[\n155 = 5(10 + 9d)\n]\nThe term ( 2 \ imes 5 ) simplifies to ( 10 ), substituting directly—this step transforms complex notation into basic arithmetic. The equation now reads:\n[\n155 = 5(10 + 9d)\n]", "---", "### Step 4: Substitute and Perform Left Multiplication\nNext, perform ( 5 \ imes (10 + 9d) ):\n[\n155 = 50 + 45d\n]\nHere, ( 5 ) multiplies the entire parenthesis ( (10 + 9d) ), distributing to replace the grouped expression with a linear sum. This substitution converts nested expressions into addition, making future steps algebraic.", "---", "### Step 5: Isolate the Variable\nSubtract 50 from both sides:\n[\n155 - 50 = 45d\n]\n[\n105 = 45d\n]\nBy substituting constants and applying inverse arithmetic, we reduce the equation to a form where ( d ) occupies one side, ready for isolation.", "---", "### Step 6: Final Substitution – Solve for ( d )\nDivide both sides by 45:\n[\nd = \frac{105}{45} = \frac{7}{3}\n]", "---", "### Conclusion\nBy carefully applying substitution—replacing nested expressions with computed values, performing arithmetic operations, and isolating the variable—we solve equations more clearly and effectively. The solution reveals:\n[\nd = \frac{7}{3}\n]\nNext time you encounter complex algebraic expressions like ( 155 = \frac{10}{2}(2 \ imes 5 + 9d) ), use substitution to break it down: numerically simplify constants, expand parentheses step-by-step, and isolate the unknown. Mastering this method transforms difficult equations into simple pathways.", "---", "Keywords:\nsolve algebra equation, substitution in equations, algebra step-by-step, simplifying linear equations, distributive property algebra, solving for variable d, algebra tutoring, equation solving techniques", "SEO Title Tag: Substituting Known Values in (155 = \frac{10}{2}(2 \ imes 5 + 9d)) — Step-by-Step Guide\nSEO Meta Description: Learn how to solve (155 = \frac{10}{2}(2 \ imes 5 + 9d)) by substituting known values and simplifying step-by-step. Perfect for students mastering algebra and equation solving.", "---\nUse this structured substitution approach whenever you solve equations—make every value count by breaking expressions into clear, manageable parts."]