Question

question
express the interval using two different representations.
x < 8 or x > 11
answer attempt 1 out of 2
interval notation:
number line:

Explanation:

Step1: Analyze \( x < 8 \)

For \( x < 8 \), in interval notation, since 8 is not included and \( x \) can go to negative infinity, it is \( (-\infty, 8) \).

Step2: Analyze \( x > 11 \)

For \( x > 11 \), 11 is not included and \( x \) can go to positive infinity, so it is \( (11, \infty) \).

Step3: Combine with "or"

Using the union symbol \( \cup \) for "or", the interval notation is \( (-\infty, 8) \cup (11, \infty) \).

Step4: Number Line Representation

• For \( x < 8 \): Draw an open circle at 8 (since 8 is not included) and shade to the left towards negative infinity.
• For \( x > 11 \): Draw an open circle at 11 (since 11 is not included) and shade to the right towards positive infinity.

Answer:

Interval Notation: \( (-\infty, 8) \cup (11, \infty) \)
Number Line: Open circle at 8, shade left; open circle at 11, shade right.