Shaniece has a points card for a movie theater.
She receives 50 rewards points just for signing up.
She earns 14.5 points for each visit to the movie theater.
She needs at least 195 points for a free movie ticket.
Write and solve an inequality which can be used to determine xx, the number of visits Shaniece can make to earn her first free movie ticket.
Let x be the number of visits Shaniece can make to earn her first free movie ticket.
She receives 50 points just for signing up, and earns 14.5 points for each visit to the movie theater. Therefore, the total number of points she will have after x visits is 50 + 14.5x.
Since she needs at least 195 points for a free movie ticket, we can write the inequality 50 + 14.5x ≥ 195.
To solve for x, we can subtract 50 from both sides of the inequality:
14.5x ≥ 145.
Then, we divide both sides of the inequality by 14.5:
x ≥ 10.
Therefore, Shaniece can make at least 10 visits to the movie theater to earn her first free movie ticket.