Substitute: \( 2(2w + w) = 60 \).

["# Mastering the Equation: How to Solve ( 2(2w + w) = 60 )", "Solving linear equations like ( 2(2w + w) = 60 ) is a foundational skill in math that applies to real-life problem-solving, from budgeting to designing projects. Whether you're a student, teacher, or self-learner, understanding how to simplify, solve, and verify such equations saves time and builds confidence. In this comprehensive guide, we'll walk through every step of solving ( 2(2w + w) = 60 ), explain key concepts, and share practical tips to help you master this kind of problem.", "## Step 1: Understand the Equation Structure", "The equation ( 2(2w + w) = 60 ) involves parentheses, multiplication, and variable terms — a common format in algebra. The expression inside the parentheses, ( 2w + w ), represents two times ( w ) plus ( w ). The whole expression is then multiplied by 2. Recognizing this structure helps identify how to simplify and isolate the variable ( w ).", "### Simplify Inside the Parentheses\nStart by combining like terms inside the parentheses:\n[\n2w + w = 3w\n]\nNow rewrite the equation:\n[\n2(3w) = 60\n]", "## Step 2: Eliminate the Multiplication", "Since ( 2 \cdot 3w = 60 ), multiply ( 2 ) and ( 3w ):\n[\n6w = 60\n]", "This step reduces the equation to a simple form where ( w ) is multiplied by 6.", "## Step 3: Isolate the Variable ( w )", "To solve for ( w ), divide both sides of the equation by 6:\n[\nw = \frac{60}{6}\n]\n[\nw = 10\n]", "## Verification: Check Your Answer", "It’s always wise to plug the solution back into the original equation. Substitute ( w = 10 ) into ( 2(2w + w) = 60 ):\n[\n2(2(10) + 10) = 2(20 + 10) = 2(30) = 60\n]\nThe left side equals the right side, confirming the solution is correct.", "## Why This Equation Matters", "Understanding how to solve ( 2(2w + w) = 60 ) reinforces key algebraic skills:\n- Combining like terms\n- Distributing multiplication across addition\n- Isolating variables\nThese skills apply to more complex equations in advanced math and real-world scenarios, such as calculating unknown quantities in sales, estimating growth rates, or balancing formulas in science.", "## Common Mistakes to Avoid", "- Forgetting to combine terms inside parentheses\n- Improperly distributing the 2 across the parentheses\n- Dividing by a negative (not applicable here, but crucial generally)\n- Skipping the verification step", "## Final Answer", "The solution to the equation ( 2(2w + w) = 60 ) is:\n[\n\boxed{w = 10}\n]", "Mastering this type of problem builds a strong foundation for algebra and beyond — so practice consistently, and soon you’ll be solving equations with confidence!", "---", "Keywords for SEO: \nSolve Substitute 2(2w + w) = 60, linear equations step by step, algebraic equation solving, how to simplify 2(2w + w), step-by-step algebra tutorial, student math resources, eliminate terms in equations, real-world equation applications", "Meta Description:\nLearn how to solve ( 2(2w + w) = 60 ) step by step. Master simplifying expressions, distributing multipliers, isolating variables, and verifying solutions with a clear explanation and real-world relevance."]