Dividiendo ambos lados por 6, obtenemos \( w = 6 \).

["SEO-Optimized Article: Simplifying Linear Equations: How Dividing Both Sides by 6 Gives ( w = 6 )", "Understanding how to simplify equations is a fundamental skill in algebra. One common operation involves dividing both sides of an equation by a number to isolate variables—an essential step in solving for unknowns. This article explores a simple yet powerful example: dividing both sides of an equation by 6 to find that ( w = 6 ).", "### The Equation: Starting Point", "Let’s consider a real-world inspired algebraic expression:\n[ \frac{12w}{6} + 3 = w ]\nWhile this equation contains multiple terms, our focus here is on isolating the variable ( w ). For clarity, suppose we simulate a scenario where both sides (representing balanced quantities, akin to equal weights or distances) are divided evenly by 6.", "### Step-by-Step Simplification", "We begin with a general linear equation structure. To demonstrate:\nDivide both sides by 6:\n[\n\frac{12w}{6} \div 6 + \frac{3}{6} = \frac{w}{6}\n]\nHowever, a clearer stated starting form for teaching purposes is:\n[\n\frac{6w + 18}{6} = 6\n]\nBut let’s return to a clean, direct path to ( w = 6 ).", "Suppose the correct form after simplifying is:\n[\n\frac{12w}{6} = 6\n]\nDividing ( 12w ) by 6 gives:\n[\n2w = 6\n]\nNow divide both sides by 2:\n[\nw = 3\n]\nWait—this yields ( w = 3 ), not 6. So how do we get ( w = 6 )?", "Let’s refine the example for accurate result.", "Correct example to yield ( w = 6 ):\nStart with:\n[\n\frac{6w}{1} = 6 \quad \ ext{or simply} \quad 6w = 12\n]\nWait—still inconsistent. Let’s define a clear, correct derivation.", "Imagine the original equation:\n[\n12w + 24 = 72\n]\nBut a simplified version inspired by dividing both sides by 6 yields a clean result.", "Suppose:\n[\n\frac{6w}{6} = 6\n]\nThen:\n[\nw = 6\n]\nBut this only works if ( \frac{6w}{6} = w ), which isolates ( w ) directly—but where does division by 6 come in?", "Now consider this accurate model:\nSuppose you have an equation:\n[\n6(2w) = 72\n]\nFirst divide both sides by 6:\n[\n2w = 12\n]\nThen divide both sides by 2:\n[\nw = 6\n]\nSo the key act is dividing sides (or terms) strategically.", "But the prompt asks: Dividiendo ambos lados por 6 obtenemos ( w = 6 ) — this holds true if the full equation is designed such that dividing both sides by 6 directly isolates ( w ).", "Let’s define it cleanly:", "Suppose:\n[\n\frac{12w}{2} = 36\n]\nWait—still leads to ( 6w = 36 \Rightarrow w = 6 ). That works—but division by 2, not 6.", "Best precise example:\nLet’s reverse-engineer cleanly.", "Suppose:\n[\n\frac{12w}{2} + 6 = 6w + 6\n]\nBut no—go back.", "Final Correct Example for Clarity:", "Let’s use:\n[\n\frac{6w}{1} = 12\n]\nThen dividing both sides by 6:\n[\nw = 12 \quad \ ext{? No.}\n]\nWait.", "Let’s solve for ( w ) directly from division:\nSuppose ( 6w = 72 ).\nThen dividing both sides by 6:\n[\nw = \frac{72}{6} = 12\n]\nStill not 6.", "But suppose:\nOriginal equation:\n[\n6w + 6 = 42\n]\nSubtract 6:\n[\n6w = 36\n]\nDivide by 6:\n[\nw = 6\n]\nYes! This uses dividing both sides by 6.", "Thus, the step-by-step is:\n1. Start with ( 6w + 6 = 42 )\n2. Subtract 6: ( 6w = 36 )\n3. Divide both sides by 6:\n[\nw = 6\n]", "### Why This Method Matters", "Dividing both sides of an equation by a constant is a foundational algebra technique. It maintains equation balance while simplifying variables—critical for solving for unknowns efficiently. Whether applied in physics, economics, or everyday problem-solving, this skill strengthens mathematical reasoning.", "### Conclusion", "Dividing both sides by 6 may seem basic, but mastering it unlocks deeper algebraic fluency. With a well-structured equation like ( 6w + 6 = 42 ), dividing both sides by 6 leads cleanly to ( w = 6 ), illustrating how simplification enables problem-solving clarity. Practice transforming equations this way—not just to find ( w ), but to build confidence in algebraic manipulation.", "Keywords: dividing both sides by 6, solving for ( w ), linear equations, algebra tutorial, simple equation simplification, algebraic manipulation, concept explained, math tips.", "---", "Meta Title:\nHow to Divide Both Sides by 6 to Solve for ( w ): Step-by-Step Algebra Example", "Meta Description:\nLearn how dividing both sides of an equation by 6 helps solve for ( w ). Step-by-step breakdown with example equation leading to ( w = 6 ). Perfect for algebra students and beginners.", "H2:\nWhy Divide Both Sides of an Equation?\nBalancing equations is key in algebra. Dividing both sides preserves equality while isolating variables—essential for clarity and solution.", "H3:\nExample: From ( 6w + 6 = 42 ) to ( w = 6 )\nSubtract 6: ( 6w = 36 )\nDivide by 6: ( w = 6 )", "H3:\nReal-World Applications\nFrom calculating unit rates to scaling recipes, dividing equations helps solve for unknowns efficiently—everyday+ math.", "H3:\nPro Tip: Simplify, Divide Denominators, Isolate the Variable\nA smart strategy in algebra: simplify expressions and divide strategically to solve.", "---", "Optimizing for search and clarity, this article teaches the action “dividiendo ambos lados por 6” with context, example, practical relevance, and clear keywords for SEO performance."]