### Video Transcript

Which of the following diagrams
represents the inequality π₯ is greater than negative three and less than or equal
to zero?

We know that when representing
inequalities on a number line, an open circle represents greater than or less
than. A closed or colored-in circle, on
the other hand, represents greater than or equal to or less than or equal to. When the circle is colored in,
weβre including that number.

In our inequality, π₯ is greater
than negative three. This means that we need an open
circle at negative three. π₯ is less than or equal to
zero. This means that we need a closed
circle at zero.

The correct answer is therefore
option (A) as there is an open circle at negative three and a closed circle at
zero.This shows the inequality π₯ is greater than negative three and less than or
equal to zero.

Option (B) has the circles the wrong
way round. This means that π₯ is greater than
or equal to negative three and less than zero. In option (C), both of the circles
are open. This means that π₯ is greater than
negative three and less than zero. In option (D), both the circles are
closed or colored in, so π₯ is greater or equal to negative three and less than or
equal to zero. In option (E), we only have one
circle. This is colored in at zero. π₯ could therefore take any value
that is less than or equal to zero. All four of these options are
incorrect.