What does the circle mean on the number line?

Which of the following diagrams represents the inequality đť‘Ą 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, we’re including that number.

In our inequality, đť‘Ą is greater than negative three. This means that we need an open circle at negative three. đť‘Ą 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 đť‘Ą is greater than negative three and less than or equal to zero.

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

Inequalities are used when a number is not equal to another value. An inequality will use one of the inequality signs:

< less than

≤ less than or equal to;

> greater than;

≥ greater than or equal to.

In algebra, the inequality will refer to a number, or range of numbers, which are either greater than, greater than or equal to, less than, or less than or equal to a fixed value.

This can be shown on a number line using lines and circles. The line indicates the range of possible values. The circle is the end point of the line.

If a circle is filled, then it is equal to or greater/less than the fixed value. If the circle is not filled, then the fixed value is not included.

a) `x < 3`; the circle is not filled so the value is less than

What does the circle mean on the number line?

b) `x ≤ 3`; the circle is filled, so the value is less than or equal to

What does the circle mean on the number line?

Two inequalities can be applied to a value at the same time. On a number line, this would be represented by a line with a circle at each end.

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What does the circle mean on the number line?
What does the circle mean on the number line?

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What does a hollow circle mean in math?

A hole on a graph looks like a hollow circle. It represents the fact that the function approaches the point, but is not actually defined on that precise value.