Question

identify the correct inequality associated with the number line.
-10 -5 0 5 10
(number line with a blue dot at 1 and an open circle at 2, line between them)
show your work here
hint: to add the number set symbols (ℝ, ℚ, ℤ, ℕ, ℂ, ℐ), type
eal\,
ational\, \integer\,
atural\, \complex\, \irrational\
options:
○ ( x < 1 ) or ( x geq 2 )
○ ( x > 1 ) and ( x leq 2 )
○ ( x leq 1 ) or ( x > 2 )
○ ( x geq 1 ) and ( x < 2 )

Explanation:

Step1: Analyze the number line

A closed - circle at a point means the point is included in the solution set (corresponds to $\leq$ or $\geq$), and an open - circle means the point is not included (corresponds to $<$ or $>$).

Step2: Determine the inequality

The closed - circle is at \(x = 1\) (so \(x\geq1\)) and the open - circle is at \(x = 2\) (so \(x<2\)). Since both conditions must be satisfied simultaneously (it's an intersection of intervals), we use "AND".

Answer:

\(x\geq1\) AND \(x < 2\)