Question

for a discount to apply, a minimum of 10 items must be purchased. which inequality describes the number of items, n, needed for the discount?
a. $n \geq 10$
b. $n \leq 10$
c. $n < 10$
d. $n > 10$

Explanation:

Step1: Understand the problem

We need to find the inequality that represents the number of items \( n \) required for a discount, given that a minimum of 10 items must be purchased.

Step2: Analyze the phrase "minimum of 10 items"

The phrase "minimum of 10 items" means that the number of items \( n \) can be 10 or more. In mathematical terms, this is represented by the inequality \( n \geq 10 \).

Let's check the other options:

• Option b: \( n \leq 10 \) means the number of items is 10 or less, which is the opposite of what we need.
• Option c: \( n < 10 \) means the number of items is less than 10, which does not satisfy the minimum requirement.
• Option d: \( n > 10 \) means the number of items is more than 10, but it excludes the case when \( n = 10 \), which is allowed since a minimum of 10 is required (so 10 should be included).

Answer:

a. \( n \geq 10 \)