Question

last year, jess saw ( x ) dramas and ( y ) comedies at the movie theater. if she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?
options: ( x + y > 8 ), ( x + y < 8 ), ( x + y leq 8 ), ( x + y geq 8 )

Explanation:

Step1: Understand the problem

Jess saw \( x \) dramas and \( y \) comedies. The total number of movies she saw is \( x + y \). She went to the theater no more than 8 times, which means the total number of movies ( \( x + y \)) is less than or equal to 8.

Step2: Analyze the inequalities

• \( x + y>8 \) means the total is more than 8, which is not correct.
• \( x + y < 8 \) means the total is less than 8, but "no more than 8" includes 8, so this is not correct.
• \( x + y\leq8 \) means the total is less than or equal to 8, which matches "no more than 8".
• \( x + y\geq8 \) means the total is more than or equal to 8, which is the opposite of what we need.

Answer:

\( x + y\leq8 \) (the third option: \( x + y\leq8 \))