Answer: (-∞, -3) U [1, ∞)
Step-by-step explanation
The portion on the left represents x < -3. The open hole means we don't include -3 itself as part of the solution. This will mean we use a parenthesis.
Think of x < -3 as -∞ < x < -3 to help see how it leads to (-∞, -3)
The portion on the right represents x ≥ 1. This time we have a closed filled in circle endpoint to include x = 1.
Think of x ≥ 1 as 1 ≤ x which expands to 1 ≤ x < ∞, to help see how it leads to [1, ∞)
Use a square bracket to include the endpoint x = 1.
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In summary, the portion on the left is x < -3 which converts to (-∞, -3)
The portion on the right is x ≥ 1 which converts to [1, ∞)
We glue these disjoint intervals together with a union symbol to get the final answer (-∞, -3) U [1, ∞)
The union symbol means "or"
We are either in interval (-∞, -3) OR we are in interval [1, ∞). We cannot be in both intervals at the same time. There isn't any common overlap between the disjoint intervals.