Solve for x*x* and graph the solution on the number line below.

minus, 11, is less than or equal to, minus, 3, x, minus, 8, or, minus, 17, is greater than or equal to, minus, 3, x, minus, 8

−11≤−3*x*−8or

−17≥−3*x*−8

Let's solve the compound inequality \( -11 \leq -3x - 8 \) or \( -17 \geq -3x - 8 \).

First, we will solve each inequality separately.

### Solving \( -11 \leq -3x - 8 \):

Add 8 to both sides:

\[ -11 + 8 \leq -3x \]

\[ -3 \leq -3x \]

Divide both sides by -3 (remember, dividing by a negative number reverses the inequality):

\[ \frac{-3}{-3} \geq \frac{-3x}{-3} \]

\[ 1 \geq x \]

This can be rewritten as:

\[ x \leq 1 \]

### Solving \( -17 \geq -3x - 8 \):

Add 8 to both sides:

\[ -17 + 8 \geq -3x \]

\[ -9 \geq -3x \]

Divide both sides by -3 (again, reversing the inequality):

\[ \frac{-9}{-3} \leq \frac{-3x}{-3} \]

\[ 3 \leq x \]

This can be rewritten as:

\[ x \geq 3 \]

### Combining the solutions:

The solution to the compound inequality is \( x \leq 1 \) or \( x \geq 3 \).

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

1. The number line will range around the values 1 and 3.
2. Since \( x \leq 1 \), we use a closed circle at 1 and shade to the left.
3. Since \( x \geq 3 \), we use a closed circle at 3 and shade to the right.

Here is the number line representation:

\[ \text{Closed circle at 1, shade left} \quad \text{Closed circle at 3, shade right} \]

```
<────● 1     3 ●────>
```

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 compound inequalities on a number line?
2. What are the steps to solve inequalities involving variables?
3. How does reversing the inequality sign work when dividing by a negative number?
4. Can you explain how to solve compound inequalities with "and" versus "or"?
5. How do you check if your solution to an inequality is correct?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve compound inequalities involving linear expressions. Understand the steps to find the solution set and graph it on a number line. Suitable for students in Grades 7-9.

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