Introduction to Compound Inequalities: Assignment

Which graph represents the inequality x ≤ -2 or x ≥ 0?

A. Line one (closed circle at -2 pointing left, closed circle at zero pointing right)

In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?

A. r > 4 and r ≤ 4.1

The compound inequality could represent which scenario?

C. Tranh must remake any sculptures that weigh less than 8.3 pounds or more than 9.8 pounds.

The compound inequality 8.00 ≤ x < 9.50 represents all values, x, for which college students are paid hourly as teacher assistants. What is another way of writing this compound inequality?

C. x ≥ 8.00 and x < 9.50

Which compound inequality can be represented by the graph below?

D. 5 < x ≤ 9

Which set of numbers is included as part of the solution set of the compound inequalityx < 6 or x > 10?

B. {-3, 4.5, 13.6, 19}

Children under 10 years and older people over 65 years receive a discount on movie tickets. Let x represent the age of a person who receives a discount. Which inequality represents the age of a child who receives a discount? Which inequality represents the age of an older person who receives a discount? Which compound inequality represents the age of a person who receives a discount?

1. 0<x<10 2. x>65 3. 0<x<10 or x>65

Layla deposits at least 25% but no more than 50% of her paycheck into a savings account. If she earns $200 per paycheck, which statements about the amount of money she deposits, s, are true? Check all that apply.

2. 50 ≤ s ≤ 100 5. She could deposit $50. 6. She could deposit $75.

Before baseball practice, Jaxon spends at least 90 minutes on homework but no more than 100 minutes. Which graph represents the scenario?

D. Line Four (closed circles at 90 and 100, line going between them both

Does changing the compound inequality x > −3 and x < 3 from "and" to "or" change the solution set? Explain.

Sample Answer: Yes, if you change the type of compound inequality, the solution set will change. The solution set of the "and" compound inequality contains values for x that satisfy both inequalities, which are values between -3 and 3. The solution set of the "or" compound inequality contains values for x that satisfy either or both inequalities, which includes all real numbers.