Question

for each part below, write an inequality to represent the given statement. then graph the inequality on the number line.
(a) the velocity of a particle is between 6 meters per second and 10 meters per second, inclusive. use v for the velocity in meters per second.
inequality:
graph:
(b) the velocity of a particle is less than 12 meters per second. use v for the velocity in meters per second.
inequality:
graph:

Explanation:

Part (a)

Step 1: Define the inequality

The velocity \( v \) is between 6 and 10 meters per second, inclusive. So the inequality is \( 6 \leq v \leq 10 \).

Step 2: Graph the inequality

On the number line (the first graph with numbers 1 - 15), we mark closed circles at 6 and 10 (since the inequality is inclusive) and shade the region between them.

Part (b)

Step 1: Define the inequality

The velocity \( v \) is less than 12 meters per second. So the inequality is \( v < 12 \).

Step 2: Graph the inequality

On the number line (the second graph with numbers 1 - 15), we mark an open circle at 12 (since the inequality is strict, \( v < 12 \) not \( v \leq 12 \)) and shade the region to the left of 12.

Answer:

(a) Inequality: \( 6 \leq v \leq 10 \); Graph: Closed circles at 6 and 10, shaded between.
(b) Inequality: \( v < 12 \); Graph: Open circle at 12, shaded to the left.