Question

Choose the correct description of the graph of the compound inequality (1 point)

x − 3 < −11 or x + 5 greater than or equal to 14.


A)A number line with a closed circle on −8, shading to the left, and an open circle on 9, shading to the right

B)A number line with an open circle on −8, a closed circle on 9, and shading in between

C)A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right

D)A number line with a closed circle on −8, an open circle on 9, and shading in between

Answer 1

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C is the answer

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Answer 2

C) A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right

Explanation:

Given compound inequality,

x − 3 < −11 or x + 5 greater than or equal to 14.

⇒ x − 3 < −11 or x + 5 ≥ 14.

⇒ x < - 11 + 3 or x ≥ 14 - 5

⇒ x < -8 or x ≥ 9

Thus, the possible values of x are all real numbers less than -8 excluding -8 and all real numbers greater than 9 including 9,

That is, x ∈ (-∞, -8 ) ∪ [ 9, ∞ )

In the number line the numbers are arranged in ascending order from left to right also in the interval the excluded number is represented by open circle and included number is represented by closed circle.

Hence, correct option is,

A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right