Questions: UNIT 2 - CHALLENGE 2.3: Ineq The number line below is correctly represented by which of the following notations? a.) [-5,8] b.) x x ≥ -5 or x ≤ 8 c.) (-∞,-5] ∪ [8, ∞)

Transcript text: UNIT 2 - CHALLENGE 2.3: Ineq The number line below is correctly represented by which of the following notations? a.) $[-5,8]$ b.) $\{x \mid x \geq-5$ or $x \leq 8\}$ c.) $(-\infty,-5] \cup[8, \infty)$

Solution

Solution Steps

Step 1: Analyze the number line

The number line shows two rays. One ray starts at -5 with a closed circle and extends to negative infinity. The other ray starts at 8 with a closed circle and extends to positive infinity.

Step 2: Write the inequality for each ray

The ray extending to negative infinity can be represented by x ≤ -5. The ray extending to positive infinity can be represented by x ≥ 8. Since the circles are closed/filled in, -5 and 8 are included as possible values for x.

Step 3: Combine the inequalities

The combined notation uses the union symbol (U) to represent that x can be in either range: (-∞, -5] U [8, ∞).