\( 2 g ( x ) = x - 3 \)

To solve the equation \( 2g(x) = x - 3 \), we first need to express \( g(x) \) in terms of \( x \). Dividing both sides by 2 gives us \( g(x) = \frac{x - 3}{2} \). This tells us that \( g(x) \) is a linear function that takes input \( x \), subtracts 3, and then divides the result by 2. To visualize this better, you might want to graph \( g(x) \). You'll find that it has a slope of \( \frac{1}{2} \), meaning for every 2 units you move in the x-direction, you'll move 1 unit up in the y-direction. Plus, it crosses the y-axis at \( -\frac{3}{2} \). Now, if you're set to apply this function in a practical context, you could think about it in terms of adjusting quantities. For instance, if \( x \) represented a temperature in Fahrenheit, \( g(x) \) could relate to a cooler temperature ideal for a pleasant evening! Just remember, whether it’s math or real life, divvying things up can make your calculations a bit sweeter!