Question

In the graph of the inequality x > 2, what does a dashed line at x = 2 indicate?

Option 1: A mistake on the graph.
Option 2: The solution region is under the dashed line.
Option 3: The solution region is to the left of the dashed line.
Option 4: The line x = 2 is not included in the solution region.

Answer 1

option 4: The line x = 2 is not included in the solution region is the correct option.

Explanation:

Given the inequality

x > 2

It is clear that the given inequality is in the simple form which indicates that x is greater than 2.

Please check the attached graph.

As x is greater than 2, thus a dashed line at x = 2 on the graph indicate indicates that x = 2 is not included in the solution region.

• Please remember that inequalities that use < or > symbols are drawn with a dashed line in order to display that line is not included in the region.

Thus, the solution to the inequality is:

`x>2\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(2,\:\infty \:\right)\end{bmatrix}`

The solution indicates that that the value of x will be greater than 2.

Please check the attached graph.

A dashed line at x = 2 on the graph indicates that x = 2 is not included in the solution region.

Hence, option 4: The line x = 2 is not included in the solution region is the correct option.