\[ 60 = 2(2w + w) \] - Dygne

["Solving the Equation 60 = 2(2w + w): A Step-by-Step Guide", "Understanding how to solve equations is essential for mastering algebra and building a strong foundation in mathematics. One common equation students encounter is:", "[
\n60 = 2(2w + w)
\n]", "This equation may look simple at first glance, but solving it reveals key algebraic principles like combining like terms, distributing multiplication, and isolating variables — all important skills for beginners and beyond.", "---", "### What Does the Equation Mean?", "The equation
\n[
\n60 = 2(2w + w)
\n]
\nrepresents a balance: the left side equals 60, and the right side is twice the sum of two expressions involving an unknown variable ( w ).", "Breaking it down:
\n- Inside the parentheses, ( 2w + w ) means we combine like terms.
\n- Outside, 2 is multiplied across the entire parenthesis.", "Our goal is to solve for ( w )—the value that makes the equation true.", "---", "### Step-by-Step Solution", "Step 1: Simplify inside the parentheses
\nStart by combining the terms inside the parentheses:
\n[
\n2w + w = 3w
\n]
\nNow the equation looks like:
\n[
\n60 = 2(3w)
\n]", "Step 2: Simplify the multiplication
\nMultiply 2 by 3w:
\n[
\n60 = 6w
\n]", "Step 3: Isolate the variable ( w )
\nTo solve for ( w ), divide both sides by 6:
\n[
\n\frac{60}{6} = w
\n]
\n[
\nw = 10
\n]", "---", "### Final Answer", "The solution to the equation ( 60 = 2(2w + w) ) is:
\n[
\n\boxed{w = 10}
\n]", "---", "### Why This Matters: Real-World Applications", "Equations like this are not just academic exercises. They model practical scenarios:
\n- Budgeting: If spending $60 (2 times some cost ( w ) multiplied by 2), solving helps determine unit prices.
\n- Physics: Calculating constants in motion or force equations often reduces to linear expressions.
\n- Computer Science: Simple linear equations form the basis of algorithms and logic flow.", "---", "### How to Solve Similar Equations Smartly", "1. Simplify inside the parentheses first—look for like terms.
\n2. Apply the distributive property when multiplication is outside.
\n3. Combine terms to streamline the equation.
\n4. Isolate the variable by undoing operations stepwise.
\n5. Verify your solution by substituting back into the original equation.", "Check:
\nPlug ( w = 10 ) back in:
\nRight side: ( 2(2(10) + 10) = 2(20 + 10) = 2(30) = 60 ) ✓", "---", "### Conclusion", "Solving ( 60 = 2(2w + w) ) is a clear demonstration of core algebraic techniques. By combining terms, distributing, and isolating the variable, you uncover that ( w = 10 ). Mastering this pattern strengthens your ability to tackle more complex problems in math, science, and everyday decision-making.", "Start practicing with similar equations—those two simple steps open the door to powerful problem-solving skills!", "---", "Keywords: solve linear equation, algebra tutorial, step-by-step solving 60 = 2(2w + w), teaching algebra, basic equation solving, algebra step-by-step, solving equations for w."]