Question

Sketch the graph of the inequality in a coordinate plane. $$ x \geq 2.5 $$

Short answer

The graphical representation of the inequality will consist of a vertical line at \(x = 2.5\), and a shaded area that starts at the line and extends to the right, representing all possible x values that are equal or larger than 2.5.

Step-by-step solution

Set up the coordinate plane

First, a two-dimensional graph (or coordinate plane) needs to be set. The horizontal line is called the x-axis and the vertical line is called the y-axis. The point where these axes intersect is known as the origin.

Sketch the line for \(x = 2.5\)

Since the inequality only involves the variable x, the result will be a vertical line at \(x = 2.5\). It might be helpful to understand that this vertical line will cross all possible values of y. It's a good start to mark the point (2.5, 0) on the x-axis, then draw a vertical line upwards and downwards from this point.

Identify the solution area

The inequality \(x \geq 2.5\) implies that x is not just 2.5, but also any value greater than 2.5. On the graph, this corresponds to an area on the right of the line \(x = 2.5\). Therefore, after drawing the vertical line, it is important to shade the region to the right of the line to show the solution to the inequality.