\( 2(4w) = 80 \Rightarrow 8w = 80 \Rightarrow w = 10 \)
["Solving ( 2(4w) = 80 ): A Step-by-Step Guide to Finding ( w = 10 )", "Understanding how to solve simple algebraic equations is essential for students, educators, and anyone working with quantitative problems. One common type of equation is a multiplication-based linear equation like ( 2(4w) = 80 ), which follows essential algebraic rules. In this article, we’ll break down how to solve ( 2(4w) = 80 ) step-by-step and explain why the solution is ( w = 10 ).", "---", "### What Does the Equation Mean?", "The equation ( 2(4w) = 80 ) expresses a real-world relationship between variables — specifically, it models a situation where something multiplied by 2 times 4 times an unknown value ( w ) equals 80. Solving for ( w ) uncovers the exact value that balances both sides of the equation.", "---", "### Step 1: Simplify the Left Side\nStart with:", "[\n2(4w) = 80\n]", "Multiply inside the parentheses:", "[\n2 \ imes 4w = 80\n]", "[\n8w = 80\n]", "This step uses the multiplication property of multiplication, where constants combine: ( 2 \ imes 4 = 8 ), resulting in ( 8w = 80 ).", "---", "### Step 2: Isolate the Variable ( w )", "Now that we have ( 8w = 80 ), divide both sides by 8 to solve for ( w ):", "[\n\frac{8w}{8} = \frac{80}{8}\n]", "[\nw = 10\n]", "By dividing both sides by the coefficient of ( w ) (which is 8), we isolate the variable cleanly — a key algebraic principle.", "---", "### What Does ( w = 10 ) Mean?", "The solution ( w = 10 ) tells us the value of the unknown variable that satisfies the original equation. Plugging back:", "[\n2(4 \ imes 10) = 2 \ imes 40 = 80\n]", "Thus, ( w = 10 ) is correct.", "---", "### Why This Equation Matters", "Equations like ( 2(4w) = 80 ) represent foundational problems in algebra, often seen in word problems involving scaling, proportion, and direct relationships. Mastering this type of equation helps build faster, accurate problem-solving skills applicable in science, finance, and engineering contexts.", "---", "### Summary of Key Steps", "| Step | Action | Result |\n|-------|-------------------------|---------------|\n| 1 | Simplify ( 2(4w) ) | ( 8w = 80 ) |\n| 2 | Solve for ( w ) | ( w = 10 ) |\n| Check | Verify solution | ( 2(4 \ imes 10) = 80 ) ✅ |", "---", "### Final Thoughts", "Solving equations step-by-step not only confirms correct answers but also builds a strong foundation in mathematical reasoning. Remember: always simplify first, isolate the variable, and verify your solution.", "Master ( 2(4w) = 80 \Rightarrow w = 10 ), and you’ll be well-prepared for more advanced algebra!", "---", "Keywords: solve algebra, linear equations, step-by-step solving, 2(4w) = 80, isolate variable, algebra tutorial, w = 10, algebra problem solving", "Meta Description: Learn how to solve ( 2(4w) = 80 ) step-by-step with full explanation, showing why ( w = 10 ) is the correct solution. Perfect for students and algebra beginners."]
