Question

write a compound inequality and an interval based on the graph shown. use x for your variable. for inequality unions, use the word or. for interval unions use the symbol ∪. inequality: interval: 5,2

Explanation:

Step1: Analyze left number line segment

The left arrow starts at an open circle at 2 and points left, so this represents all values less than 2.
$x < 2$

Step2: Analyze right number line segment

The right arrow starts at an open circle at 3 and points right, so this represents all values greater than 3.
$x > 3$

Step3: Combine into compound inequality

Since the graph shows two separate sets, use "or" to combine the inequalities.
$x < 2 \text{ or } x > 3$

Step4: Convert to interval notation

For $x < 2$, the interval is $(-\infty, 2)$; for $x > 3$, the interval is $(3, \infty)$. Use $\cup$ to represent the union.
$(-\infty, 2) \cup (3, \infty)$

Answer:

Inequality: $x < 2 \text{ or } x > 3$
Interval: $(-\infty, 2) \cup (3, \infty)$