Question

1. a. select all numbers that are solutions to the inequality (k > 5). 4 5 6 5.2 5.01 0.5 b. draw a number line to represent this inequality. 2. a sign on the road says, “speed limit: 60 miles per hour.” a. let (s) be the speed of a car. write an inequality that matches the information on the sign. b. draw a number line to represent the solutions to the inequality. c. could 60 be a value of (s)? explain your reasoning.

Explanation:

Step1: Identify solutions for $k > 5$

Numbers greater than 5 are solutions. 4 is less than 5, 5 is equal to 5, 0.5 is less than 5. But 6, 5.2 and 5.01 are greater than 5.

Step2: Write inequality for speed - limit

The speed limit is 60 miles per hour, so the speed $s$ of a car should satisfy $s\leq60$ (not $s > 60$ as wrongly written in the question).

Step3: Analyze if 60 is a solution for speed - limit inequality

Since the inequality is $s\leq60$, 60 is a solution because it satisfies the "less - than or equal to" condition.

Answer:

1. a. 6, 5.2, 5.01
2. a. $s\leq60$
3. c. Yes, because the inequality is $s\leq60$ and 60 satisfies this inequality as it is equal to 60. For the number - line drawing parts (1. b and 2. b), here is the general way:

• For 1. b: Draw a number line, mark 5 with an open circle (since $k>5$ does not include 5) and shade the part of the number line to the right of 5.
• For 2. b: Draw a number line, mark 60 with a closed circle (since $s\leq60$ includes 60) and shade the part of the number line to the left of 60.