So, \( 2(5w) = 90 \) which simplifies to \( 10w = 90 \).

["Simplify the Equation: How to Solve ( 2(5w) = 90 ) Step by Step", "Solving basic algebraic equations is a foundational skill in mathematics, especially when learning variables and linear expressions. One common problem students encounter is solving equations such as ( 2(5w) = 90 ), which simplifies neatly to ( 10w = 90 ). In this SEO-optimized guide, we’ll walk you through solving this equation, highlight its importance, and explore why mastering such steps boosts your math confidence.", "---", "### Understanding the Equation: ( 2(5w) = 90 )", "At first glance, the equation ( 2(5w) = 90 ) may seem complex because it contains multiplication inside parentheses. However, breaking it down step by step is key to simplification and solving.", "The left side, ( 2(5w) ), means “2 times 5w,” or simply multiplying 5w by 2. Using the distributive property or recognizing direct multiplication, ( 2 \ imes 5w = 10w ). So we rewrite the equation as:", "[\n10w = 90\n]", "---", "### Solving for ( w ): Simplifying and Isolating the Variable", "To find the value of ( w ), we need to isolate the variable. Since ( w ) is multiplied by 10, we divide both sides of the equation by 10:", "[\nw = \frac{90}{10}\n]", "[\nw = 9\n]", "This simple division reveals that ( w = 9 ), the solution to the equation.", "---", "### Why Is This Simplification Important?", "Breaking down ( 2(5w) = 90 ) into ( 10w = 90 ) demonstrates key algebraic concepts:", "- Order of Operations (PEMDAS): Parentheses before multiplication clarify how to simplify expressions.\n- Combining Like Terms: Multiplying constants together streamlines the equation.\n- Inverse Operations: Dividing by 10 reverses multiplication, allowing us to solve for ( w ).", "Mastering such steps not only helps in solving basic equations but also builds a strong foundation for more advanced algebra, including solving multi-step equations and systems of equations.", "---", "### Real-World Application: How ( w = 9 ) Matters", "Suppose you’re planning a workshop and need to prepare materials for ( w ) participants—where each participant receives 5 workbooks. If the total number of workbooks needed is 90, how many participants ( w )?", "The equation mirrors real life:\n[\n2(5w) = 90\n]\n[\n10w = 90 \Rightarrow w = 9\n]", "So, 9 participants require the materials—applying math to everyday planning.", "---", "### Tips to Master Equation Solving", "- Always simplify before solving: Reduce expressions inside parentheses and apply operators step by step.\n- Use inverse operations carefully: Multiply or divide both sides appropriately.\n- Check your work: Plug ( w = 9 ) back into the original equation:\n [\n 2(5 \cdot 9) = 2(45) = 90 \quad \ ext{✓ Equation holds}\n ]", "---", "### Conclusion", "Solving ( 2(5w) = 90 ) simplifying to ( 10w = 90 ) is more than a math drill—it's a vital step toward logical reasoning and problem-solving. With practice, this process becomes intuitive, empowering learners to confidently tackle linear equations in academics and daily life.", "---", "Keywords:\nlinear equations, solve for w, simplify algebra, 2(5w) = 90, algebra tutorial, equation solving steps, basic algebra, math tutorial, step-by-step equation solve, logarithmic thinking, math fundamentals", "Meta Description:\nLearn how to simplify ( 2(5w) = 90 ) into ( 10w = 90 ), solve for ( w ), and understand key algebra concepts with step-by-step guidance perfect for students and math beginners.", "---", "Start solving equations today—mastering foundational math builds confidence for advanced topics and real-world challenges!"]