Solve for xx and graph the solution on the number line below.3≥x−7>
1

Let's solve the compound inequality \( 3 \geq x - 7 > 1 \).

First, break it into two separate inequalities and solve each:

1. \( 3 \geq x - 7 \)
2. \( x - 7 > 1 \)

### Solving \( 3 \geq x - 7 \):

Add 7 to both sides:

\[ 3 + 7 \geq x \]

\[ 10 \geq x \]

This can be rewritten as:

\[ x \leq 10 \]

### Solving \( x - 7 > 1 \):

Add 7 to both sides:

\[ x - 7 + 7 > 1 + 7 \]

\[ x > 8 \]

### Combining the solutions:

\[ 8 < x \leq 10 \]

Now, let's graph this solution on the number line:

1. The number line will range around 8 and 10.
2. Since \( x > 8 \), we use an open circle at 8.
3. Since \( x \leq 10 \), we use a closed circle at 10.
4. Shade the region between 8 and 10.

Here is the number line representation:

\[ \text{Open circle at 8} \quad (---) \quad \text{Closed circle at 10} \]

```
8 ∘─────────────────● 10
```

Would you like more details or have any questions about this solution?

Here are 5 questions you might want to ask:

1. How do you graph inequalities on a number line?
2. What is a compound inequality?
3. How do you solve a system of inequalities?
4. Can you explain interval notation for the solution set?
5. How do you verify the solution of an inequality?

**Tip:** When solving compound inequalities, treat each part separately before combining the solutions for a complete answer.

Learn how to solve the compound inequality 3 ≥ x - 7 > 1 step-by-step and graph the solution on a number line. This problem covers key concepts including inequalities, compound inequalities, and number line graphing. Suitable for students in Grades 7-9.

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