### Instruction: Find all real numbers $x$ such that \[3 \le \frac{x}{2x-5} < 8.\](Give your answer in interval notation.).### Response: Let's first look at the left side of the inequality.
We can multiply both sides by $2x - 5$ to get $3(2x-5) \le x$.
That simplifies to $6x - 15 \le x$.
So $5x \le 15$, and $x \le 3$.
Now let's look at the right side of the inequality.
We can multiply both sides by $2x - 5$ to get $8(2x-5) > x$.
That simplifies to $16x - 40 > x$.
So $15x > 40$, and $x > 8/3$.
So the solution set is $8/3 < x \le 3$.