Question

for problems 11–13, write and graph an inequality for each situation.

1. the width w is less than 10 inches.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1. the truck has a weight t of more than 2 tons.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1. the temperature t was below 20 °c.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Explanation:

Problem 11

Step1: Translate the situation to an inequality

The width \( w \) is less than 10 inches, so the inequality is \( w < 10 \).

Step2: Graph the inequality

On the number line, we draw an open circle at 10 (since \( w \) is not equal to 10) and shade to the left of 10 to represent all values less than 10.

Step1: Translate the situation to an inequality

The truck's weight \( t \) is more than 2 tons, so the inequality is \( t > 2 \).

Step2: Graph the inequality

On the number line, we draw an open circle at 2 (since \( t \) is not equal to 2) and shade to the right of 2 to represent all values greater than 2.

Step1: Translate the situation to an inequality

The temperature \( t \) was below \( 20^\circ \text{C} \), which means \( t < 20 \).

Step2: Graph the inequality

On the number line, we draw an open circle at 20 (since \( t \) is not equal to 20) and shade to the left of 20 to represent all values less than 20.

Answer:

Inequality: \( w < 10 \)
Graph: Open circle at 10, shade left.

Problem 12