["## Solve ( 2(w + 4w) = 90 ): Step-by-Step Guide to Find the Value of ( w )", "Understanding how to solve linear equations is essential in algebra and helps build problem-solving skills for more advanced math. One common type of equation students encounter is expressions involving parentheses, like ( 2(w + 4w) = 90 ). In this article, we’ll walk through solving this equation step-by-step, explain key algebra concepts, and highlight why mastering such equations matters.", "### Understanding the Equation: ( 2(w + 4w) = 90 )", "The equation ( 2(w + 4w) = 90 ) contains:", "- Parentheses: Grouping terms inside for simplification
\n- Coefficients: Multiplied with variables (e.g., ( w ), ( 4w ))
\n- Equality: The equation balances at both sides (90 on the right)", "Our goal is to isolate ( w ) and find its value.", "---", "### Step 1: Combine Like Terms Inside the Parentheses", "Inside the parentheses ( w + 4w ), both terms contain ( w ), so they are like terms. Add them:", "[
\nw + 4w = 5w
\n]", "Now substitute back into the equation:", "[
\n2(5w) = 90
\n]", "---", "### Step 2: Simplify the Left Side", "Multiply 2 by ( 5w ):", "[
\n2 \ imes 5w = 10w
\n]", "So the equation becomes:", "[
\n10w = 90
\n]", "---", "### Step 3: Solve for ( w ) by Isolating the Variable", "To find ( w ), divide both sides by 10:", "[
\nw = \frac{90}{10} = 9
\n]", "---", "### Step 4: Verify the Solution", "Plug ( w = 9 ) back into the original equation to check:", "[
\n2(w + 4w) = 2(9 + 4 \ imes 9) = 2(9 + 36) = 2 \ imes 45 = 90
\n]", "The equation balances, confirming ( w = 9 ) is correct.", "---", "### Why This Equation Matters", "Solving equations like ( 2(w + 4w) = 90 ) reinforces:", "- Algebraic manipulation: Combining like terms and applying the distributive property
\n- Balancing equations: Maintaining equality by applying the same operation on both sides
\n- Simplification skills: Reducing expressions step-by-step for easier solving
\n- Real-world applications: Useful in budgeting, speed calculations, and comparison problems where relationships are linear", "---", "### Summary", "- Start by combining like terms inside parentheses.
\n- Apply multiplication (distributive property) to simplify expressions.
\n- Perform inverse operations to isolate the variable.
\n- Always verify your solution by substituting it back into the original equation.", "Mastering such equations builds a strong foundation for future algebra topics like systems of equations, linear inequalities, and function analysis.", "---", "### Key Takeaway", "The solution to ( 2(w + 4w) = 90 ) is:", "[
\n\boxed{w = 9}
\n]", "Keep practicing with similar equations to strengthen your algebraic fluency!", "---", "Search Terms for SEO Optimization:
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\n- Step-by-step solution to ( 2(w + 4w) = 90 )", "---", "Effective algebra solving enhances critical thinking and problem-solving skills — essential for students, educators, and lifelong learners. Start with this simple equation and build confidence for more complex challenges!"]
