Question

Which one of the following graphs represents a compound inequality?
Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Definition: A pair of inequalities (compound inequality) are connected by "and"/"or" statement.
Option (a):
A closed circle at $4$ and the red line goes to the left, indicating that $x$ is less than or equal to $4.$
$\to$ $x\le 4$

Option (b):

A closed circle at $4$ and the red line goes to the right, indicating that $x$ is greater than or equal to $4.$
$\to$ $x\ge 4$

Option (c):

A closed circle at $4$ indicating that $x$ is equal to $4.$
$\to$ $x=4$

Option (d):

A closed circle at $4$, $7$ and the red line goes from 4 to 7, indicating that $x$ is less than or equal to $4,$ but greater than or equal to $7.$
$\to$ $x\ge 4$ and $x\le 7$
Hence, Option d is correct.