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.
(-oo,-6]u[-4,00)

Answer 1

To complete the table, we will express the given interval in inequality notation, graph it, and then provide it in interval notation.

### Given Interval:
\((-∞, -6] \cup [-4, ∞)\)

### Inequality Notation:
1. For the interval \((-∞, -6]\):
- Inequality: \(x \leq -6\)

2. For the interval \([-4, ∞)\):
- Inequality: \(x \geq -4\)

### Graphs:
1. For \(x \leq -6\):
- Graph: An open arrow pointing left from -6 with a closed circle on -6 (indicating that -6 is included).

2. For \(x \geq -4\):
- Graph: An open arrow pointing right from -4 with a closed circle on -4 (indicating that -4 is included).

### Interval Notation:
- \((-∞, -6] \cup [-4, ∞)\) (this is already given)

### Completed Table:

| Inequality Notation | Graph | Interval Notation |
|---------------------|----------------------------------|-------------------------------|
| \(x \leq -6\) |  | \((-∞, -6]\) |
| \(x \geq -4\) |  | \([-4, ∞)\) |

### Combined Interval Notation:
The combined interval notation for the entire set would be:
- \((-∞, -6] \cup [-4, ∞)\)

Note: As a text-based AI, I cannot create actual graphics, so you can visualize the graph as described or use graphing software/tools for a visual representation.