### Instruction: How many integers satisfy $-4 \le 2x+1 \le 6$?### Response: I want to find the possible values of x that make the inequality true.
To do that, I can start by subtracting 1 from all sides, which gives me $-5 \le 2x \le 5$.
Then, I can divide everything by 2, which gives me $-2.5 \le x \le 2.5$.
Now, I can see that the smallest integer that satisfies this inequality is -2, and the largest is 2.
So, the possible values of x are -2, -1, 0, 1, and 2.
That means there are 5 integers that satisfy the inequality.