The only answer choice that accurately represents the graph is x < −2 or x ≥ 4.
To visualize the graph, let's consider each inequality separately:
x < −2: This inequality represents all x-values to the left of −2, excluding −2 itself.
x ≥ 4: This inequality represents all x-values to the right of 4, including 4 itself.
Combining these two inequalities, we can see that the graph includes all x-values less than −2 and all x-values greater than or equal to 4. This is represented by the answer choice x < −2 or x ≥ 4.
The other answer choices do not accurately represent the graph:
−2 < x ≤ 4: This inequality includes all x-values between −2 and 4, including −2 and 4 themselves. However, the graph excludes −2 and only includes x-values less than −2 and x-values greater than or equal to 4.
−2 ≤ x < 4: This inequality includes all x-values between −2 and 4, excluding 4 itself. However, the graph includes x-values greater than or equal to 4 as well.
x ≤ −2 or x > 4: This inequality includes all x-values less than or equal to −2 or all x-values greater than 4. However, the graph only includes x-values less than −2 and x-values greater than or equal to 4.
Therefore, the only answer choice that accurately represents the graph is x < −2 or x ≥ 4.