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Which graph on a plane (not along the real number line) from below belongs to the inequality: \( x \leq 6 \)

Ask by Morgan Henry. in the United States
Feb 21,2025

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Tutor-Verified Answer

Answer

The correct graph is the one with a solid vertical line at \( x = 6 \) and the area to the left of the line shaded or filled.

Solution

To determine which graph on a plane corresponds to the inequality \( x \leq 6 \), we need to understand what this inequality represents. 1. **Understanding the Inequality**: - The inequality \( x \leq 6 \) means that we are interested in all points where the x-coordinate is less than or equal to 6. - This describes a vertical line at \( x = 6 \) and includes all points to the left of this line. 2. **Graphing the Inequality**: - The line \( x = 6 \) itself will be a solid line because the inequality includes equality (the "less than or equal to" part). - The region that satisfies the inequality will be all the points to the left of this line, including the line itself. 3. **Identifying the Correct Graph**: - Look for a vertical line at \( x = 6 \) that is solid (not dashed) and shaded or filled to the left side of the line. If you have specific graphs to choose from, you would look for the one that matches this description. If you can provide the graphs, I can help you identify the correct one.

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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!

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