Question

The inequality graphed below represents the ages, a, of players on a baseball team.

Which inequality represents the same ages?

12 < a ≤ 18
12 ≤ a < 18
12 > a ≤ 18
12 ≥ a < 18

Answer 1

The inequality that represents the same ages as the graphed inequality is 12 ≤ a < 18.

Let's break down the given inequalities to understand why 12 ≤ a < 18 is the correct representation:

1. 12 < a ≤ 18: This inequality means that the ages of the players are greater than 12 but less than or equal to 18. However, the graph does not include the point where a = 12, so this inequality does not match the given graph.

2. 12 ≤ a < 18: This inequality means that the ages of the players are greater than or equal to 12 but less than 18. This matches the given graph, as the point where a = 12 is included, but the point where a = 18 is not included.

3. 12 > a ≤ 18: This inequality means that the ages of the players are less than 12 but less than or equal to 18. However, the graph does not include the point where a = 18, so this inequality does not match the given graph.

4. 12 ≥ a < 18: This inequality means that the ages of the players are less than or equal to 12 but less than 18. However, the graph does not include the point where a = 12, so this inequality does not match the given graph.

Therefore, the correct inequality that represents the same ages as the graphed inequality is 12 ≤ a < 18.Step-by-step explanation: