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The compound inequality given is:

\[
x \leq -27 \quad \text{or} \quad x \geq -23
\]

This inequality consists of two parts:
1. \( x \leq -27 \) means all values of \( x \) less than or equal to -27.
2. \( x \geq -23 \) means all values of \( x \) greater than or equal to -23.

To graph this:

- For \( x \leq -27 \), you will plot a closed circle at -27 and shade the line to the left (representing all values less than or equal to -27).
- For \( x \geq -23 \), you will plot a closed circle at -23 and shade the line to the right (representing all values greater than or equal to -23).

This is an **"or"** compound inequality, so the graph will include both regions. The shading will extend left from -27 and right from -23.

Here’s what you need to do on the number line provided:
- Place a closed circle at -27.
- Place a closed circle at -23.
- Draw an arrow to the left from -27, indicating all values less than or equal to -27.
- Draw an arrow to the right from -23, indicating all values greater than or equal to -23.

Would you like a more detailed breakdown of the steps or further explanation?

Here are 5 related questions to help deepen your understanding:
1. What is the difference between "and" and "or" compound inequalities?
2. How would the graph change if the inequality was \( x < -27 \) or \( x > -23 \)?
3. What happens if both parts of the compound inequality are exclusive (i.e., no equal signs)?
4. Can you describe a real-life scenario where you might use an "or" inequality?
5. How would the graph look if it were an "and" inequality instead of "or"?

**Tip:** Always double-check whether the inequality includes the equals sign (≤, ≥), which tells you whether to use a closed circle (inclusive) or open circle (exclusive) when graphing.

Graph the compound inequality x ≤ -27 or x ≥ -23.

Learn how to graph the compound inequality x ≤ -27 or x ≥ -23 using a number line. This problem covers key algebraic concepts related to inequalities and number lines. Suitable for students in Grades 7-9.

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