Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

As you read and work through Explorations 1 and 2 and Communicate Your Answer on page 45, be sure to question yourself so that you understand what the statements are saying. 

For example, Statement a states, “The temperature t in Sweden is at least –10°C.” Ask yourself if the temperature could be –20°C. That would be a false possibility because –20 is less than –10. The temperature must be –10°C or more.

Sometimes when you translate a verbal phrase or context into symbols, the variable may end up on the right side of the inequality symbol. Example: 80 points was the lowest score on the test; 80 < p. Rewrite the inequality so that the variable is read first (left side of inequality). In doing so, the direction of the inequality symbol must be switched; p > 80.

Once you finish Explorations 1 and 2 and Communicate Your Answer, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 45)

1. t ≥ –10°C
   
2. e ≤ 2407 ft
   

Exploration 2 (page 45)

1. x ≥ 1; one and all numbers greater than one
2. x > 1; all numbers greater than one
3. x ≤ 1; one and all numbers less than one
4. x < 1; all numbers less than one

Communicate Your Answer (page 45)

3. An inequality can indicate the largest or smallest value for a quantity.
4. a. Sample answer: The judge’s score is less than 3.5.
   b. Sample answer: The time in the pool was at most 6 hours.
   c. Sample answer: The temperature is greater than –2°C.
   d. Sample answer: The profit was at least $10.

Section 2-1 Lesson (pages 46-49)

Remember that ≥ and ≤ will have a closed circle on the number line, but > and < will have an open circle.

Now read over examples 1 through 4.

Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 46-49)

1. b < 30.4
2. ≥ 2k – 4
3. yes
4. no
5. yes
6. no
7. 
8. 
9. 
10. 
11. x ≥ –6