To determine the inequality that represents the number of coins in Michael's collection, let's break down the information given:
Michael has more than 20 coins in his collection.
The keyword here is "more than," which indicates that the number of coins (let's denote it by [tex]\( x \)[/tex]) is greater than 20. We need to translate "more than 20" into a mathematical inequality.
- Option A: [tex]\( x < 20 \)[/tex]
This option states that the number of coins is less than 20, which contradicts the information given. Thus, it is not correct.
- Option B: [tex]\( x > 20 \)[/tex]
This option states that the number of coins is greater than 20. This matches the given information that Michael has more than 20 coins. Therefore, this is a possible correct answer.
- Option C: [tex]\( x + 20 \)[/tex]
This option is not an inequality; it's an expression. It doesn't provide a relationship that we can use to compare [tex]\( x \)[/tex] with 20. Hence, it cannot be the correct answer.
- Option D: [tex]\( x = 20 \)[/tex]
This option states that the number of coins is exactly 20, which again contradicts the information given. Thus, it is not correct.
Based on the above analysis, the correct inequality representing the number of coins in Michael's collection is given by:
[tex]\[ \boxed{x > 20} \][/tex]
This inequality correctly reflects that Michael has more than 20 coins.
