Question

question
express the interval using two different representations.
answer attempt 2 out of 2
(-∞, -2) ∪ (11, ∞)
inequality notation:
number line:

Explanation:

Step1: Analyze the interval \((-\infty, -2) \cup (11, \infty)\)

The interval \((-\infty, -2)\) means all real numbers less than \(-2\), and \((11, \infty)\) means all real numbers greater than \(11\).

Step2: Write the inequality notation

For \((-\infty, -2)\), the inequality is \(x < -2\). For \((11, \infty)\), the inequality is \(x > 11\). Combining these with "or" (since it's a union of two intervals), we get \(x < -2\) or \(x > 11\).

Step3: Represent on the number line

• For \(x < -2\): We draw an open circle at \(-2\) (because \(-2\) is not included in the interval) and shade the line to the left of \(-2\).
• For \(x > 11\): We draw an open circle at \(11\) (because \(11\) is not included in the interval) and shade the line to the right of \(11\).

Answer:

• Inequality Notation: \(x < -2\) or \(x > 11\)
• Number Line: Open circle at \(-2\) with shading left, open circle at \(11\) with shading right.