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
x≤-3

Answer 1

Here’s how to complete the table for the inequality \( x \leq -3 \):

| **Inequality Notation** | **Graph** | **Interval Notation** |
|-------------------------|-----------|-----------------------|
| \( x \leq -3 \) |  (Closed circle at -3, shading to the left) | \((- \infty, -3]\) |

### Explanation:
- **Inequality Notation**: The inequality is \( x \leq -3 \) meaning \( x \) can take any value less than or equal to \(-3\).
- **Graph**: The graph would have a closed circle at \(-3\) (since it includes \(-3\)) and shading to the left to indicate all numbers less than \(-3\).
- **Interval Notation**: In interval notation, this is represented as \((- \infty, -3]\), which indicates all numbers from negative infinity up to and including \(-3\).