To determine the minimum number of visits [tex]\( v \)[/tex] that Valeria needs to earn her first free movie ticket, let's break down the information step-by-step and form the correct inequality.
1. Initial Points from Signing Up:
Valeria starts with 35 points.
2. Points Earned per Visit:
Valeria earns 11.5 points for each visit to the movie theater.
3. Points Required for a Free Movie Ticket:
Valeria needs at least 55 points for a free movie ticket.
Now, let's form an equation to represent this scenario:
- Points from signing up: [tex]\( 35 \)[/tex]
- Points earned after [tex]\( v \)[/tex] visits: [tex]\( 11.5v \)[/tex]
Total points after [tex]\( v \)[/tex] visits can be represented as:
[tex]\[ 35 + 11.5v \][/tex]
Valeria wants to earn at least 55 points. Therefore, we form the inequality:
[tex]\[ 35 + 11.5v \geq 55 \][/tex]
This is the inequality that can be used to determine the minimum number of visits [tex]\( v \)[/tex] Valeria needs to earn her first free movie ticket.
Thus, out of the given options, the correct inequality is:
[tex]\[ 35 + 11.5v \geq 55. \][/tex]
