1. The problem is to solve the inequality $$\frac{2}{x} \leq -1$$. 2. To solve this, we first note that $$x \neq 0$$ because division by zero is undefined. 3. Multiply both sides of the inequality by $$x^2$$ (which is always positive) to avoid reversing the inequality sign: $$2x \leq -x^2$$ 4. Rearranging terms: $$x^2 + 2x \leq 0$$ 5. Factor the quadratic expression: $$x(x + 2) \leq 0$$ 6. The product $$x(x + 2)$$ is less than or equal to zero when $$x$$ is between the roots: $$-2 \leq x \leq 0$$ 7. However, since $$x=0$$ is not allowed (division by zero), the solution is: $$-2 \leq x < 0$$ Final answer: $$\boxed{-2 \leq x < 0}$$