Question

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Answer 1

Answer: A)  $x < -4 \ \text{ or } \ x \ge 3$

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Explanation:

The left portion of the graph is $x < -4$ to indicate values smaller than -4. We exclude the endpoint -4 due to the open hole. So we don't have "or equal to" as part of the inequality sign.

In contrast, we do include the endpoint 3 since there's a filled in endpoint here. The right side of the shaded graph shows values that are 3 or larger. So that's why we have $x \ge 3$ which says "x is greater than or equal to 3".

Put those two pieces together and we end up with $x < -4 \ \text{ or } \ x \ge 3$

You must use "or" instead of "and" because they mean different things. Saying $x < -4 \ \text{ and } \ x \ge 3$ is not correct because there are no numbers that are both less than -4 and greater than or equal to 3 at the same time. Visually there are no numbers that are to the left of -3 and also to the right of 3 at the same time.