Adrian has a points card for a movie theater. He receives 20 rewards points just for signing up.
He earns 2.5 points for each visit to the movie theater.
He needs at least 35 points for a free movie ticket.

Write and solve an inequality which can be used to determine vv, the number of visits Adrian can make to earn his first free movie ticket.

v ≥ 6

This means that Adrian needs to do at least 6 visits.

Step-by-step explanation:

First, we know that he gets 20 points just for signing up, so he starts with 20 points.

Now, if he makes v visits, knowing that he gets 2.5 points per visit, he will have a total of:

20 + 2.5*v

points.

And he needs to get at least 35 points, then the total number of points must be such that:

points ≥ 35

and we know that:

points = 20 + 2.5*v

then we have the inequality:

20 + 2.5*v  ≥ 35

Now we can solve this for v, so we need to isolate v in one side of the equation:

2.5*v ≥ 35 - 20 = 15

2.5*v ≥ 15

v ≥ 15/2.5 = 6

v ≥ 6

So he needs to make at least 6 visits.

60.96438

step-by-step explanation:

2nd one in the first row is correct