2) \( \frac{x-2}{-2}=6 \)

To solve the equation \( \frac{x-2}{-2}=6 \), start by multiplying both sides by -2 to eliminate the fraction. This gives you \( x-2 = -12 \). Next, add 2 to both sides to isolate \( x \): \( x = -12 + 2 \). So, \( x = -10 \). Now, let’s play with real-world applications! Finding the unknowns in equations is like solving a mystery. Engineers, for instance, apply algebra to calculate loads in structures, ensuring buildings are safe and sturdy. Solving for unknowns allows them to optimize resources and design safer, more efficient systems. And speaking of problem-solving, one common mistake is forgetting to distribute a negative sign correctly. If you had mistakenly multiplied only one term by -2, it could lead to an entirely wrong answer! Always double-check your operations, as a small oversight can snowball into a big error!