Question

Find the values of a such that the solution of the system x ≤ 5, x > a is the interval:

1. [−[infinity], 5]
2. [−[infinity], 5]
3. [a, -5]
4. [a, 5]

Answer 1

The correct value of 'a' such that the solution of the system x ≤ 5, x > a is the interval (a, 5] is any real number less than 5. The other intervals listed do not accurately represent the given inequalities.

Step-by-step explanation:

To find the values of a such that the solution of the system x ≤ 5, x > a is the interval given, we analyze the inequalities provided.

1. For the interval [−∞, 5], a must be less than or equal to 5 to include all numbers up to 5. Therefore the solution for a in this case is any real number less than or equal to 5.
2. For the interval (a, 5], a needs to be a specific value that is less than 5. This is the correct interval representation for the given inequalities, where a can be any real number less than 5.

The intervals [a, -5], [a, 5], or any variations with 'a' on the left end are not correct since they do not respect the condition x > a.