Question

jace has a points card for a movie theater.

• he receives 50 rewards points just for signing up.
• he earns 14.5 points for each visit to the movie theater.
• he needs at least 310 points for a free movie ticket.

which inequality can be used to determine x, the minimum number of visits jace needs to earn his first free movie ticket?
answer

• 14.5(x + 50) ≥ 310
• 310 ≤ 14.5x + 50
• 310 ≥ 14.5x + 50
• 14.5(x + 50) ≤ 310

Explanation:

Step1: Analyze total points

Jace gets 50 points for signing up and 14.5 points per visit. So total points after \( x \) visits is \( 14.5x + 50 \).

Step2: Set up inequality

He needs at least 310 points, meaning total points \( \geq 310 \), or \( 310 \leq 14.5x + 50 \).

Answer:

B. \( 310 \leq 14.5x + 50 \)