Final Answer:
The set x ∈ ℤ, and -5 < x ≤ 4 can be expressed using the listing method as {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4}.
Step-by-step explanation:
In this set, we are representing the integers (ℤ) within the specified range where -5 is less than x and x is less than or equal to 4. The expression "x ∈ ℤ" denotes that x belongs to the set of integers. To express this using the listing method, we list all the integers that satisfy the given conditions. The set starts with -5 (as -5 < x) and includes all the integers up to and including 4 (as x ≤ 4).
Starting with -5, we increment by one until we reach 4, including each integer in the set. The resulting set is {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4}. This set encompasses all the integers within the specified range, satisfying both the condition that -5 is less than x and x is less than or equal to 4.
In mathematical terms, this set can be represented as x ∈ ℤ, and -5 < x ≤ 4, where the vertical bar "|" is read as "such that." The use of the listing method provides a clear and concise way to express the set by enumerating its elements, making it easily understandable.