Question

Choose the correct description of the graph of the compound inequality

x − 1 less than or greater to 12 or 2x greater than or equal to 30.

A) A number line with an open circle on 13, shading to the left, and an open circle on 15, shading to the right

B) A number line with a closed circle on 13, shading to the left, and a closed circle on 15, shading to the right

C) A number line with an open circle on 13, an open circle on 15, and shading in between

D) A number line with a closed circle on 13, a closed circle on 15, and shading in between

Answer 1

i think you meant x − 1 is less than or equal to 12 or 2x greater than or equal to 30.
x<=13 or x>=15, both closed going opposite directions so B

Answer 2

Option: B is the correct answer.

B) A number line with a closed circle on 13, shading to the left, and a closed circle on 15, shading to the right

Explanation:

We are given a compound inequality as:

(1)
`x-1\leq 12`

This could also be written as:

`x\leq 13`

This means that the region is: (-∞,13]

(2)
`2x\geq 30`

On dividing both side of the inequality by 2 we get:

`x\geq 15`

This means that the region is: [15,∞)

Hence, the region that we obtain in the number line is

(-∞,13]∪[15,∞)

Hence, the shaded region is to the left of 13 with the closed circle at 13 and to the right of 15 with closed circle at 15.