The library needs at least 15 people to sign up for an event in order to run it. Currently, 3 people have signed up, and the library expects 2 more people to sign up each day. After how many days will the library be sure it can run the event? Write an inequality that could be used to solve this problem.

To solve this problem, we need to determine how many days it will take for the number of people signed up to reach at least 15.

Let \( x \) be the number of days after today.

Currently, 3 people have signed up, and the library expects 2 more people to sign up each day. Therefore, the number of people signed up after \( x \) days can be expressed as:

\[ 3 + 2x \]

We want this expression to be at least 15, so we can write the inequality:

\[ 3 + 2x \geq 15 \]

Now, we can solve this inequality for \( x \):

1. Subtract 3 from both sides: \[ 2x \geq 12 \]

2. Divide both sides by 2: \[ x \geq 6 \]

Thus, the library will be sure it can run the event after 6 days.

In summary, the inequality we used to solve this problem is:

\[ 3 + 2x \geq 15 \]