Question

The number line below represents which combined inequality?

number line with a closed circle on negative 2, shading to the left and a closed circle on 4, shading to the right

x greater than or equal to −2 or x less than or equal to 4
x greater than or equal to −2 and x less than or equal to 4
x less than or equal to −2 or x greater than or equal to 4
x less than or equal to −2 and x greater than or equal to 4

Answer 1

closed circle means that the inequality conatains 'equal'

Its C

Answer 2

Answer with explanation:

Description about Number line:

→Number line with a closed circle on negative 2, shading to the left and a closed circle on 4, shading to the right.------(1)

⇒Taking the fragment of the above sentence,"till shading to left" and describing it in terms of Inequality

x ≤ -2-------(2)

x∈(-∞,-2]

And,Now writing another half of the sentence--(1) in terms of inequality,

x≥4---------(3)

x∈[4,∞)

Why i have ,taken equal to sign into consideration, the reason is that the two circles which are marked on -2 and 4, tells us that these points must be considered,while writing inequality

Combining ,(2) and (3),we get

⇒x less than or equal to −2 or x greater than or equal to 4