Substitute: \(2(3w + w) = 64\).
["# Solving the Equation: Substitute and Solve (2(3w + w) = 64)", "Mathematics often requires us to manipulate and simplify expressions to uncover unknown values — a fundamental skill in algebra. One essential type of problem involves substituting expressions into equations and solving for the variable. In this article, we explore how to solve the equation:", "[\n2(3w + w) = 64\n]\nas a practical example of substitution and simplification in equation solving.", "---", "## Step-by-Step Substitution and Simplification", "### Step 1: Understand the expression inside the parentheses", "Inside the parentheses, we have (3w + w). This is a key substitution point — combining like terms simplifies the equation before solving.", "[\n3w + w = (3 + 1)w = 4w\n]\nSo the original equation becomes:\n[\n2(4w) = 64\n]", "### Step 2: Simplify the left-hand side", "Multiply (2) by (4w):\n[\n2 \ imes 4w = 8w\n]\nNow the equation is simplified to:\n[\n8w = 64\n]", "### Step 3: Isolate the variable (w)", "To solve for (w), divide both sides of the equation by 8:\n[\nw = \frac{64}{8} = 8\n]", "---", "## Why This Substitution Matters", "This example demonstrates a core algebraic technique: substituting combined terms to simplify an equation, then isolating the variable. Substitution in this context means replacing (3w + w) with (4w), which reduces complexity and speeds up solving.", "This skill is crucial not only in basic algebra but also in higher-level math, physics, engineering, and computer science, where equations grow more complex.", "---", "## Final Answer", "The solution to the equation (2(3w + w) = 64) is:\n[\n\boxed{w = 8}\n]", "---", "### Pro Tips for Mastering This Problem Type", "- Always combine like terms inside parentheses first to simplify the expression before solving.\n- Use distributive property to eliminate parentheses after combining terms.\n- Isolate the variable using inverse operations to uncover the unknown.", "Practice similar substitutions and simplifications regularly — they form the backbone of algebraic fluency.", "---", "Keywords: algebra substitution, solve equation step-by-step, simplify (3w + w), how to solve (2(3w + w) = 64), algebraic problem-solving, distribute and combine like terms, equation solving techniques.", "Meta Description: Learn how to solve (2(3w + w) = 64) by substituting and simplifying. Step-by-step explanation for students and learners mastering basic algebra."]
