To graph the inequality $x > 2$ on a number line, you follow these steps:

1. Draw a Number Line: Start by drawing a horizontal line and marking a few key points, such as $0$, $1$, $2$, $3$, etc.

2. Identify the Boundary Point: The boundary for the inequality $x > 2$ is at $x = 2$. Place a point at $2$ on the number line.

3. Determine the Type of Circle at $x = 2$: Since the inequality is strictly greater than (not greater than or equal to), use an open circle at $x = 2$ to show that $2$ itself is not included in the solution.

4. Shade the Correct Region: Shade the line to the right of $x = 2$ to indicate that all numbers greater than $2$ are included in the solution set.

Graph

<--------------------o==================>
-3 -2 -1  0  1  2  3  4  5 ...

In this graph:

• The "o" at $x = 2$ represents an open circle, meaning $x = 2$ is not part of the solution.
• The shaded line ("===") to the right of $2$ indicates that all numbers greater than $2$ satisfy the inequality.

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Related Questions:

1. How would you graph $x \geq 2$ on a number line?
2. What does $x < -3$ look like on a number line?
3. How do you represent $2 \leq x < 5$ on a number line?
4. What changes if the inequality is $x \neq 2$?
5. How would you solve a compound inequality like $1 < x \leq 4$?

Tip: Remember that an open circle is used for inequalities that do not include the boundary point (e.g., $x > 2$), and a closed circle is used when the boundary is included (e.g., $x \geq 2$).