https://file.aiquickdraw.com/mathbot/file/1727367959697elct3zyr.jpg

Let's solve the inequality \(5x - 25 > -15\).

### Step 1: Isolate the variable \(x\)
Add 25 to both sides of the inequality:

\[
5x - 25 + 25 > -15 + 25
\]
\[
5x > 10
\]

### Step 2: Solve for \(x\)
Now, divide both sides by 5:

\[
x > \frac{10}{5}
\]
\[
x > 2
\]

### Solution: 
The solution to the inequality is \(x > 2\), meaning the values of \(x\) are greater than 2.

### Step 3: Match the correct graph
The number line should show an open circle at \(x = 2\) (since \(x\) is greater than 2, but not equal to 2) and shading to the right, indicating that the values of \(x\) are greater than 2.

Looking at the options:
- **Option A** shows \(x > 2\) with an open circle at 2 and shading to the right, which matches the solution.

Therefore, **Option A** is the correct answer.

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Do you need further details or have any questions?

Here are five related questions:
1. How would the graph change if the inequality was \(5x - 25 \geq -15\)?
2. What happens to the solution if the inequality sign changes to \(<\)?
3. Can you explain how to solve an inequality with a negative coefficient on \(x\)?
4. How can we graph a compound inequality like \(2x + 1 \geq 5 \text{ and } x - 3 < 6\)?
5. What is the difference between solving inequalities and solving equations?

**Tip**: Always check if you need an open or closed circle when graphing solutions for inequalities!

Which number line shows the solution of 5x - 25 > -15?

Learn how to solve the inequality 5x - 25 > -15 step by step and find the correct number line that represents the solution. The problem involves solving a linear inequality and graphing its solution on a number line, suitable for students in Grades 6-8.

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