A: Show the inequalities on the number line.                                                                   x>2               -5 -4 -3 -2 -1 0 1 2 3 4 5                                                                                                                       

To represent the inequality \( x > 2 \) on a number line, you need to indicate all the numbers greater than 2. Here's how you can do it:

1. Draw a number line with the given range from \(-5\) to \(5\).
2. Mark the point \(2\) on the number line.
3. Since \(x > 2\) does not include the number \(2\) itself (strict inequality), use an open circle at \(2\) to indicate that \(2\) is not part of the solution.
4. Shade the portion of the number line to the right of \(2\) to show all numbers greater than \(2\).

The number line will look like this:

\[
\begin{array}{c}
\text{Number Line:} \\
\underline{-5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad \circ 2 \quad \longrightarrow 3 \quad 4 \quad 5}
\end{array}
\]

The open circle at \(2\) and the arrow pointing to the right indicate all the numbers greater than \(2\).

Would you like more details or have any questions? 

Here are 5 related questions to further explore this concept:

1. How would you represent \( x \geq 2 \) on a number line?
2. What does the inequality \( x < -3 \) look like on a number line?
3. How can you represent a compound inequality like \( -1 \leq x < 4 \) on a number line?
4. What does an inequality with no solutions look like on a number line?
5. How would you represent \( x \neq 0 \) on a number line?

**Tip:** When using an open circle on a number line, it indicates that the number at that point is not included in the set of solutions. A closed (filled) circle indicates that the number is included.

Learn how to represent the inequality x > 2 on a number line with a detailed step-by-step solution. This problem covers key concepts in inequalities and number line representation, focusing on the open circle notation and shading. Suitable for students in Grades 7-9.

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