91Ó°ÊÓ

Let's understand the Cartesian plane first. Imagine a piece of paper with a grid drawn on it. The horizontal line is called the x-axis, and the vertical line is called the y-axis. These two lines intersect at a point called the origin, which has coordinates (0,0).
The Cartesian plane is divided into four quadrants by these axes. The right side of the y-axis and above the x-axis is the first quadrant, where both x and y are positive.
Moving counterclockwise, the second quadrant is to the left of the y-axis and above the x-axis (x is negative, y is positive).
The third quadrant is below the x-axis and to the left of the y-axis (both x and y are negative).
The fourth quadrant is below the x-axis and to the right of the y-axis (x is positive, y is negative).
This grid helps us plot points and graph equations or inequalities. Each point is written as (x, y), where x is the horizontal position and y is the vertical position.

A vertical line is a straight line that goes up and down on a graph. When we talk about a line being vertical, it means that every point on this line has the same x-coordinate.
For example, the line given by the equation x = 3 is a vertical line because no matter what y value you choose, x is always 3.
In the exercise, we draw this line at x = 3 to show the boundary for the inequality. Since the inequality is x greater than or equal to 3, we draw the line as a solid line. This solid line shows that x can be exactly 3, not just greater than 3.
Vertical lines are easy to draw on the Cartesian plane because you just need to find the point where x equals the given value and draw a straight line up and down through that point.

Shading regions on a graph helps to show all the possible solutions to an inequality. In our given inequality, we need to show all x values that are greater than or equal to 3.
This means we shade the entire area to the right side of the vertical line x = 3. Every point in this shaded region satisfies the inequality.
If x was less than 3, we would shade the left side instead.
When shading, make sure you don’t miss any part of the region. For the inequality x greater than or equal to 3, include points on the line, since ‘equal to’ is part of the condition.
Just remember: the goal of shading is to make clear all the points that are solutions to the inequality.