Simplifying: \( 2(3w + 5) = 60 \) → \( 6w + 10 = 60 \) → \( 6w = 50 \) → \( w = \frac{50}{6} = \frac{25}{3} \).
["Simplifying Linear Equations: Solve ( 2(3w + 5) = 60 ) Step-by-Step", "Solving linear equations is a fundamental skill in algebra that lays the groundwork for more advanced math topics. One common challenge students face is simplifying equations step by step to isolate the variable and find its value. In this article, we’ll explore how to simplify the equation:", "[\n2(3w + 5) = 60\n]", "to its simplest form and solve for ( w ), with a final answer expressed as a simplified fraction.", "---", "### Step 1: Expand the Parentheses\nStart by distributing the 2 across the terms inside the parentheses:", "[\n2 \cdot 3w + 2 \cdot 5 = 60\n]", "[\n6w + 10 = 60\n]", "This simplification step is crucial—it removes parentheses and clarifies the equation.", "---", "### Step 2: Eliminate the Constant Term\nTo isolate the term with the variable ( w ), subtract 10 from both sides:", "[\n6w + 10 - 10 = 60 - 10\n]", "[\n6w = 50\n]", "This step gives you the coefficient of ( w ) and isolates the variable term.", "---", "### Step 3: Solve for ( w )\nNow divide both sides by 6:", "[\nw = \frac{50}{6}\n]", "Simplify the fraction by dividing numerator and denominator by 2:", "[\nw = \frac{25}{3}\n]", "---", "### Final Answer:\n[\n\boxed{w = \frac{25}{3}}\n]", "---", "### Why This Process Matters\nBreaking down equations step by step helps students understand the logic behind solving for unknowns. Each move—distributing, subtracting, dividing—serves a clear purpose in isolating the variable. Mastering this procedure builds confidence and accuracy, key components for success in algebra and beyond.", "If you're learning equations, remember:\n- Always simplify both sides before solving.\n- Keep operations balanced by applying the same step to both sides.\n- Reduce fractions early to avoid complex calculations later.", "Simplifying ( 2(3w + 5) = 60 ) to ( \frac{25}{3} ) is a clear example of how algebra becomes manageable when approached systematically. Keep practicing, and these equations won’t just simplify—they’ll become intuitive."]
