27. The solution of \( \frac{1-3 x}{2} \leq 5-2 x \) or \( x-7 \geq 2 \) is A. \( x \leq 9 \). B. \( x \geq 9 \). C. \( x \neq 9 \).

To solve the inequalities, let's take a look at each one separately. Starting with \( \frac{1-3x}{2} \leq 5-2x \): 1. Multiply through by 2 to eliminate the fraction: \( 1 - 3x \leq 10 - 4x \). 2. Rearranging gives \( x \leq 9 \). Now for the second inequality \( x - 7 \geq 2 \): 1. Adding 7 to both sides gives \( x \geq 9 \). Combining both parts, we find that \( x \leq 9 \) from the first inequality and \( x \geq 9 \) from the second inequality leads us to conclude that \( x = 9 \). Thus, the solution is \( x = 9 \), which means \( x \neq 9 \) is incorrect. So the answer is **none of the options are fully correct, as it should be specifically \( x = 9 \)**. For a little fun on the side, did you know that math has its own special language? It's a bit like a secret code that only those brave enough to solve equations get to use! And speaking of equations, don’t forget the importance of checking your work—if you miss a simple sign or a number during your calculations, you might just end up in a goofy solution-land!