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

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

Step-by-step 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

(a) and (b) are not equivalent

(c) is equivalent

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine an equivalent or nonequivalent expression

We have:

Apply law of indices

This is not equivalent to

We have:

Apply law of indices

This is not equivalent to

We have:

Apply law of indices

Evaluate the numerator

This is an equivalent expression