Question

graph each inequality on a number line. (example 2)

1. $-20>b$
2. $d\geq12$
3. $a>-8$
4. $18\leq c$
5. there will be fewer than 50 tickets sold for a charity event. write and graph an inequality that represents the number of tickets t that will be sold for the event. (example 3)
6. students have no more than 90 minutes to complete a test. write and graph an inequality that represents the time in minutes m students have to complete the test. (example 3)

Explanation:

Step1: Analyze the inequality for problem 9

The phrase "fewer than" means less than. So the inequality for the number of tickets \(t\) is \(t < 50\).

Step2: Graph the inequality \(t < 50\)

On a number line, draw an open circle at \(50\) (because \(50\) is not included) and shade to the left of \(50\).

Step3: Analyze the inequality for problem 10

The phrase "no more than" means less than or equal to. So the inequality for the time \(m\) is \(m\leq90\).

Step4: Graph the inequality \(m\leq90\)

On a number line, draw a closed circle at \(90\) (because \(90\) is included) and shade to the left of \(90\).

Answer:

1. Inequality: \(t < 50\); Graph: Open - circle at \(50\), shade left.
2. Inequality: \(m\leq90\); Graph: Closed - circle at \(90\), shade left.