Solve the following rational inequality: \(-\frac{2}{x-3} \geq 1\)

Step 1 ：Step 1: Rewrite the inequality as \(-\frac{2}{x-3} - 1 \geq 0\)

Step 2 ：Step 2: Find a common denominator for the fractions, which is \(x-3\), and rewrite the inequality as \(-\frac{2}{x-3} - \frac{x-3}{x-3} \geq 0\)

Step 3 ：Step 3: Simplify the inequality to get \(-\frac{x+2}{x-3} \geq 0\)

Step 4 ：Step 4: Set the numerator and denominator equal to zero to find the critical points. We get \(x=-2\) and \(x=3\)

Step 5 ：Step 5: Test the intervals \((-\infty, -2)\), \((-2, 3)\), and \((3, \infty)\) to find the solution set. We find that when \(x \in (-\infty, -2)\) or \(x \in (3, \infty)\), the inequality holds true.