Question 9 Solve the equation. \( \frac{9}{x-4}=1 \)

To solve the equation \( \frac{9}{x-4}=1 \), start by multiplying both sides by \( x-4 \) (assuming \( x \neq 4 \) to avoid division by zero): \( 9 = x - 4 \). Next, add 4 to both sides: \( x = 9 + 4 \), which simplifies to \( x = 13 \). So, the solution is \( x = 13 \). But wait, there's some cool history behind equations like this! The concept of solving equations dates back to ancient civilizations, with the Babylonians using geometric methods around 2000 B.C. They didn’t have algebra as we know it, but they were tackling similar problems using their own clever techniques—imagine channeling their inner mathematicians without the luxury of modern symbols! As for the practical side, this equation represents a common scenario in fields like physics or finance, where variables need to be isolated to understand relationships. For example, if \( x \) represents time and you want to know how long it takes to reach a certain point when considering distance (9 units away) minus a starting point (4 units), you can easily get to your answer with basic algebra just like we did here. Plus, you'll impress your friends with your math skills!