Question

Graph the compound inequality.
x ≥ 2 and x 8
Plot the endpoints

Answer 1

I’m missing the comparison sign in “x 8.” Which did you mean: ≤, <, >, or ≥?

Here are the common possibilities and how to graph each (endpoints shown):

1) If x ≥ 2 and x ≤ 8:
- Solution: 2 ≤ x ≤ 8
- Interval notation: [2, 8]
- Graph: closed (filled) dots at 2 and 8, shade the segment between them.
- ASCII: ---●================●---

2) If x ≥ 2 and x < 8:
- Solution: 2 ≤ x < 8
- Interval notation: [2, 8)
- Graph: closed dot at 2, open circle at 8, shade between.
- ASCII: ---●================o---

3) If x ≥ 2 and x > 8:
- Combine gives x > 8 (because >8 implies ≥2)
- Interval notation: (8, ∞)
- Graph: open circle at 8, arrow to the right.
- ASCII: ---o==================>

4) If x ≥ 2 and x ≥ 8:
- Combine gives x ≥ 8
- Interval notation: [8, ∞)
- Graph: closed dot at 8, arrow to the right.
- ASCII: ---●==================>

Tell me which sign you meant and I’ll give a neat final graph.