Which graph on a plane (not along the real number line) from below belongs to the inequality: \( x \leq 6 \)
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The Deep Dive
Imagine a vertical line cutting through the number 6 on the x-axis. This line serves as a boundary. The inequality \( x \leq 6 \) means that you're interested in all the points that lie to the left of this line, shrouded by the entire vertical expanse of the graph. Hence, the area to the left of and including the line at \( x = 6 \) is filled in or shaded to signify all the valid solutions. Additionally, remember that this inequality is inclusive of the line itself, which means that every point on the line \( x = 6 \) is part of the solution set. When you visualize it, you can think of a friendly neighborhood with everyone on the left side of that line allowed to join the party, while those on the right must stay out!