\(x = -\frac{80}{2 \times -2} = 20\).

["# Solving (x = -\frac{80}{2 \ imes -2} = 20): A Clear Step-by-Step Explanation", "Equations can often appear intimidating at first glance, but breaking them down into manageable steps makes solving them simple and clear. One such example is solving (x = -\frac{80}{2 \ imes -2} = 20). In this article, we'll explore how to interpret this equation, simplify the expression, and verify that (x = 20) is indeed the correct solution. Whether you’re a student learning algebra or someone looking to sharpen your problem-solving skills, understanding this process will help you confidently tackle similar challenges.", "## Understanding the Equation: Breaking It Down", "At first glance, (x = -\frac{80}{2 \ imes -2} = 20) may look complex, but it’s simply a fraction expression simplified step by step. The equation replaced division by rewriting the denominator:", "Original Equation:\n[\nx = -\frac{80}{2 \ imes -2}\n]", "Step 1: Simplify the Denominator\nStart by simplifying the expression in the denominator:\n[\n2 \ imes -2 = -4\n]\nSo the equation becomes:\n[\nx = -\frac{80}{-4}\n]", "Step 2: Simplify the Fraction\nNow divide 80 by -4. Remember, dividing a negative number by a negative number yields a positive result:\n[\n\frac{80}{-4} = -20\n]\nBut since there’s a negative sign in front of the fraction:\n[\n-\left( \frac{80}{-4} \right) = -(-20) = 20\n]", "Thus,\n[\nx = 20\n]", "## How Is (x = 20) the Correct Solution?", "Algebra relies on maintaining equivalence throughout simplification. Every step preserves the equation’s truth, ensuring (x = 20) is the verified solution. Substituting (x = 20) back into the original expression confirms this:", "[\nx = -\frac{80}{\left(2 \ imes -2\right)} = -\frac{80}{-4} = 20\n]", "This verifies the solution is accurate.", "## Why This Equation Matters", "This problem illustrates key algebraic principles: simplifying expressions, correctly handling signs in division, and verifying solutions. Mastering these concepts enables you to solve more complex equations efficiently. The final result, (x = 20), is not just a number—it’s the unique value that satisfies the original expression.", "## Final Thoughts", "Solving linear equations like (x = -\frac{80}{2 \ imes -2} = 20) requires patience and attention to detail. By breaking down the problem into dividable steps and confirming each simplification, you build confidence in algebra. Practice similar problems to strengthen your skills—soon, even complex equations will feel straightforward.", "Understanding that (x = 20) is the accurate solution reinforces how algebra transforms abstract expressions into clear, verifiable truths. Keep practicing, and mastering these foundational skills will serve you well in both math and real-world problem-solving.", "---", "Key Takeaways from This Explanation:\n- Always simplify expressions step-by-step to avoid errors.\n- Remember negative division yields a positive result.\n- Substitute the solution back into the original equation to verify correctness.\n- Foundational algebra builds the basis for advanced math topics.", "This structured approach ensures clarity and correctness—key elements for mastering algebraic concepts."]