Question

express the interval using two different representations. (-∞, -5) ∪ (7, ∞) answer attempt 1 out of 2 inequality notation: blank number line: number - line image with numbers from - 12 to 12

Explanation:

Step1: Recall interval - to - inequality conversion

The open - interval $(-\infty,-5)$ in inequality notation is $x < - 5$, and the open - interval $(7,\infty)$ in inequality notation is $x>7$. Since it is a union, the combined inequality notation is $x < - 5$ or $x>7$.

Step2: Represent on number line

On the number line, we draw an open circle at $x=-5$ and shade to the left for $x < - 5$, and we draw an open circle at $x = 7$ and shade to the right for $x>7$.

Answer:

Inequality Notation: $x < - 5$ or $x>7$
Number Line: Draw an open circle at $-5$ and shade to the left, draw an open circle at $7$ and shade to the right.