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|≥2
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|≥2
Answers
GPT-4o mini
To complete the table for the inequality \( |x| \geq 2 \), we will represent it in three formats: Inequality Notation, Graph, and Interval Notation.
### Inequality Notation
The inequality \( |x| \geq 2 \) means that \( x \) is less than or equal to -2 or greater than or equal to 2. This can be written in two parts:
1. \( x \leq -2 \)
2. \( x \geq 2 \)
### Graph
To graph this:
- For \( x \leq -2 \): draw a solid line extending to the left from -2 with a closed circle at -2.
- For \( x \geq 2 \): draw a solid line extending to the right from 2 with a closed circle at 2.
### Interval Notation
In interval notation, this inequality is represented as:
\[
(-\infty, -2] \cup [2, \infty)
\]
### Complete Table
| Inequality Notation | Graph | Interval Notation |
|-----------------------------------|---------------------------|-------------------------|
| \( |x| \geq 2 \) |  | \( (-\infty, -2] \cup [2, \infty) \) |
Please replace the `![Graph]` placeholder text with an appropriate graph illustration, which depicts the requirements stated above. If you are graphing by hand or using a graphing tool, ensure that closed circles are at -2 and 2, with arrows extending outwards in both directions.
### Inequality Notation
The inequality \( |x| \geq 2 \) means that \( x \) is less than or equal to -2 or greater than or equal to 2. This can be written in two parts:
1. \( x \leq -2 \)
2. \( x \geq 2 \)
### Graph
To graph this:
- For \( x \leq -2 \): draw a solid line extending to the left from -2 with a closed circle at -2.
- For \( x \geq 2 \): draw a solid line extending to the right from 2 with a closed circle at 2.
### Interval Notation
In interval notation, this inequality is represented as:
\[
(-\infty, -2] \cup [2, \infty)
\]
### Complete Table
| Inequality Notation | Graph | Interval Notation |
|-----------------------------------|---------------------------|-------------------------|
| \( |x| \geq 2 \) |  | \( (-\infty, -2] \cup [2, \infty) \) |
Please replace the `![Graph]` placeholder text with an appropriate graph illustration, which depicts the requirements stated above. If you are graphing by hand or using a graphing tool, ensure that closed circles are at -2 and 2, with arrows extending outwards in both directions.