Question

express the interval using two different representations. (-∞, -5) ∪ (7, ∞) answer attempt 1 out of 2 , , ) (, (, ) -∞ ∞ ∪ < > ≤ ≥ or inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

Step1: Recall inequality - interval relation

The open - interval $(-\infty,-5)$ corresponds to the inequality $x < - 5$, and the open - interval $(7,\infty)$ corresponds to the inequality $x>7$. The union symbol $\cup$ in interval notation corresponds to the word "or" in inequality notation.

Step2: Write inequality notation

The inequality notation for the interval $(-\infty,-5)\cup(7,\infty)$ is $x < - 5$ or $x>7$.

Step3: Describe number - line representation

On the number line, for $x < - 5$, we have an open circle at $-5$ and an arrow pointing to the left. For $x>7$, we have an open circle at $7$ and an arrow pointing to the right.

Answer:

Inequality Notation: $x < - 5$ or $x>7$
Number Line: Open circle at $-5$ with arrow to the left, open circle at $7$ with arrow to the right.