Okay, let's see. The problem is: Three plus the reciprocal of a number equals 7 divided by that number. What is the number? Hmm. Alright, so I need to find a number, let's call it x, such that when I take three and add the reciprocal of x, it equals 7 divided by x. Let me write that down to make sure I understand it correctly.

So, the equation should be: 3 + (1/x) = 7/x. Right? Let me check that. The reciprocal of a number is 1/x, so three plus that is 3 + 1/x. And that's supposed to equal 7 divided by the number, which is 7/x. Yeah, that seems right.

Now, I need to solve for x. Let's start by writing the equation again:

3 + (1/x) = 7/x.

Okay, so the first step is to get all the terms involving x on one side and the constants on the other. Hmm. Let's subtract 1/x from both sides to get rid of the reciprocal on the left. That would give:

3 = 7/x - 1/x.

Wait, 7/x minus 1/x is (7 - 1)/x, which is 6/x. So the equation simplifies to:

3 = 6/x.

Now, solving for x. If 3 equals 6 divided by x, then x must be 6 divided by 3, right? Because if 3 = 6/x, then multiplying both sides by x gives 3x = 6, so x = 6/3 = 2. So x is 2. Let me check that.

Plugging x = 2 back into the original equation: 3 + (1/2) should equal 7/2. Let's compute both sides. Left side: 3 + 0.5 = 3.5, which is 7/2. Right side: 7/2 is also 3.5. So that works. So x = 2 is the solution. Hmm, that seems straightforward. But wait, let me make sure I didn't skip any steps or make any mistakes in my algebra.

Starting again: 3 + 1/x = 7/x. Subtract 1/x from both sides: 3 = 6/x. Multiply both sides by x: 3x = 6. Divide by 3: x = 2. Yep, that's correct. And checking the solution works. So the answer should be 2. Wait, but let me think if there's another way to approach this problem or if there's a possibility of another solution.

Another approach: Let's multiply both sides of the original equation by x to eliminate the denominators. So:

Original equation: 3 + (1/x) = 7/x.

Multiply both sides by x:

3x + 1 = 7.

Subtract 1 from both sides:

3x = 6.

Divide by 3:

x = 2. Same result. So that's consistent. So regardless of the method, we get x = 2. Therefore, the number is 2. 

Wait, but let me check if there's any restriction on x. Since we have reciprocals, x can't be zero. But 2 is not zero, so that's fine. So there's only one solution here, x = 2. 

Alternatively, could there be another solution if we considered different steps? Let's see. Suppose we rearrange the original equation differently. Let's take 3 + 1/x = 7/x. Subtract 3 from both sides: 1/x = 7/x - 3. Then, 1/x = (7 - 3x)/x. Multiply both sides by x: 1 = 7 - 3x. Then, subtract 7: 1 - 7 = -3x => -6 = -3x => x = 2. Same result. So all methods lead to x = 2. 

Therefore, I think the solution is correct. The number is 2. Let me just recap to make sure I didn't make any calculation errors. 

First approach: Combine like terms by subtracting 1/x from both sides, leading to 3 = 6/x, then solving for x gives 2. 

Second approach: Multiply through by x to eliminate denominators, leading to 3x + 1 = 7, then solving for x gives 2. 

Third approach: Rearranging the equation differently, still leading to x = 2. 

All methods confirm the same answer. So I can be confident that the number is indeed 2.
Therefore, the number is $\boxed{2}$.
</think>