Question

What solution set does the number line graph?

(1 point)
Responses

x≤−3 and x≥−3
x less-than-or-equal-to negative 3 and x greater-than-or-equal-to negative 3

x<−3 and x>3
x less than negative 3 and x greater than 3

x≤−3 or x≥−3
x less-than-or-equal-to negative 3 or x greater-than-or-equal-to negative 3

x<−3 or x>3

Answer 1

To accurately determine which solution set corresponds to the number line graph, we need to clarify the interpretations of each response based on the descriptions provided.

Here’s a breakdown of the options:

1. **x ≤ -3 and x ≥ -3**
- This actually means just x = -3, as both conditions need to be true simultaneously.

2. **x < -3 and x > 3**
- This set represents numbers that are less than -3 or greater than 3, which would not be adjacent.

3. **x ≤ -3 or x ≥ -3**
- This includes all numbers less than or equal to -3 and also all numbers greater than or equal to -3. This is essentially all real numbers since it covers everything on the number line.

4. **x < -3 or x > 3**
- This indicates numbers that are either less than -3 or greater than 3, which are the two intervals that do not overlap.

Without seeing the actual number line graph, I can't tell you definitively which option is correct, but each interpretation offers different ranges of number sets.

If you are looking for a solution set that includes all the real numbers, then option 3 (x ≤ -3 or x ≥ -3) is the likely answer. If the graph shows two distinct regions (left of -3 and right of 3), then option 4 would be the right one.

Please provide more specific details about the number line graph for a precise answer!