Question

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

Answer 1

We want numbers that satisfy both x ≥ 2 and x < 8, i.e. the intersection of [2, ∞) and (-∞, 8) is [2, 8).

Interval notation: [2, 8)

Graph on a number line:
- Put a closed (solid) dot at 2 because x ≥ 2.
- Put an open circle at 8 because x < 8.
- Shade the line between 2 and 8.

ASCII sketch:

...0---1---●2===3===4===5===6===7===○8---9---10...
(where ● = closed dot at 2, ○ = open circle at 8, === = shaded region)

So the solution is all x with 2 ≤ x < 8.