Question

Complete the table below. Each row represents an inequality in Inequality Notation, as a Graph and in Interval Notation

For Graphing: If the symbol in the inequality is < or > , use an open circle.
If the symbol in the inequality is ≤ or ≥, use a closed circle.
|x|≥3
interval notation

Answer 1

To complete the table for the inequality \( |x| \geq 3 \):

1. **Inequality notation**:
\[ |x| \geq 3 \]

This means that \( x \) can either be less than or equal to -3 or greater than or equal to 3.

2. **Graph**:
- For \( x \leq -3 \), use a closed circle at -3 and shade to the left.
- For \( x \geq 3 \), use a closed circle at 3 and shade to the right.

```plaintext
<---------● ●-------->
-3 3
```

3. **Interval Notation**:
\[ (-\infty, -3] \cup [3, \infty) \]

So, filling in the table looks like this:

| Inequality Notation | Graph | Interval Notation |
|---------------------|--------------------------------|-------------------------|
| \( |x| \geq 3 \) | <---------● ●--------> | \( (-\infty, -3] \cup [3, \infty) \) |