Question

The number line below is correctly represented by which of the following notations?

Answer 1

A

Explanation:

This is saying that all of the answer are less than -2 or equal or greater than 6.

x < -2 mean that the -2 is not included as a solution.

x ≥ 6 means that 6 is part of the solution.

Answer 2

a) x

Explanation:

A number line is a graphical representation of numbers placed along a straight line. It extends infinitely in both directions, allowing for the representation of any real number.

Graphing on a number line:

• An open circle indicates that the endpoint is not included in the interval.
• A closed circle indicates that the endpoint is included in the interval.
• A shaded region between two points represents all the numbers within that range.
• An arrow pointing in a specific direction indicates that the set of numbers extends infinitely in that direction.

From observation of the given number line:

• There is an open circle at -2. This indicates that -2 is not included in interval. The shading to the left from -2 represents that the interval extends indefinitely in the negative direction towards negative infinity. In summary, the open circle and shading indicate that all numbers less than -2 are included in the interval.

• There is a closed circle at 6. This indicates that 6 is included in the interval. The shading to the right from 6 represents that the interval extends indefinitely in the positive direction towards positive infinity. In summary, the closed circle and shading indicate that all numbers greater than or equal to 6 are included in the interval.

Interval notation:

• ( or ) : Use parentheses to indicate that the endpoint is excluded.
• [ or ] : Use square brackets to indicate that the endpoint is included.

Therefore, the interval notation to represent the given number line is:

• (-∞, -2) ∪ [6, ∞)

Inequality notation:

• < means "less than".
• > means "more than".
• ≤ means "less than or equal to".
• ≥ means "greater than or equal to".

Therefore, the interval notation to represent the given number line is:

• x < -2 or x ≥ 6