To accurately answer your question, I would need to know how the number line is represented or what it looks like. However, based on the options you've provided, I'll explain the meaning of each so you can identify the correct one based on the graph.
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x ≤ -3 and x ≥ -3: This suggests a point at -3 that includes all numbers less than -3 and also includes -3 itself. This is redundant since "and" would imply that x can be both less than and greater than -3 at the same time.
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x ≤ -3 or x ≥ -3: This indicates that all numbers less than or equal to -3 and all numbers greater than or equal to -3 are included. This covers all real numbers.
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x < -3 and x > 3: This means that you want numbers less than -3 and numbers greater than 3. These are two separate intervals.
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x < -3 or x > 3: This implies numbers that are either less than -3 or greater than 3, forming two separate intervals.
To determine the correct option, look at the number line graph:
- If it includes everything (left arrow and right arrow, covering all real numbers), the correct choice would be "x ≤ -3 or x ≥ -3."
- If it shows two separate intervals (one to the left of -3 and one to the right of 3), then it should be "x < -3 or x > 3."
Please check the graph against these interpretations to find the correct answer.