Section P.2 Homework

1. List the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Select all that apply.)

A. Natural Numbers

B. Integers

C. Rational Numbers

D. Irrational Numbers

2.  List the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Select all that apply.)

A. Natural Numbers

B. Integers

C. Rational Numbers

D. Irrational Numbers

3.  State the property of real numbers being used. 3 + 9 = 9 + 3

1. Distributive Property
2. Associative Property of Addition    
3. Commutative Property of Addition
4. Associative Property of Multiplication
5. Commutative Property of Multiplication 

4.   State the property of real numbers being used. 4(6 + 7) = (6 + 7)4

1. Distributive Property
2. Associative Property of Addition    
3. Commutative Property of Addition
4. Associative Property of Multiplication
5. Commutative Property of Multiplication 

5.  State the property of real numbers being used.  (x + 4y) + 3z = x + (4y + 3z)

1. Associative Property of Addition 
2. Commutative Property of Multiplication      
3. Commutative Property of Multiplication      
4. Distributive Property 
5. Commutative Property of Addition 

6.   State the property of real numbers being used.  7(A + B) = 7A + 7B

1. Associative Property of Addition 
2. Commutative Property of Multiplication     
3. Associative Property of Multiplication 
4. Distributive Property 
5. Commutative Property of Addition 

7.  State the property of real numbers being used.  (8x + 7) 2 = 16x + 14

1. Associative Property of Addition
2. Associative Property of Multiplication    
3. Distributive Property
4. Commutative Property of Multiplication
5. Commutative Property of Addition 

8.  Rewrite the expression using the given property of real numbers.  Associative Property of Multiplication,  3(6x)

9.  Use properties of real numbers to write the expression without parentheses.  –

1. −9x + 27y
2. −9x − 27y
3.  −18xy
4.  18xy
5.  9x + 27y

    

    

10.  Perform the indicated operations.

A.

B.

11.  Place the correct symbol (<, >, or =) in the space.

A. 

___

B.

___

C.

12. Place the correct symbol (<, >, or =) in the space.

$$\begin{gathered} A. \frac{5}{3} \_\_\_ 1.67 \\ B. \frac{5}{3} \_\_\_ –1.67 \\ C. \left|1.67\right| \_\_ \left|–1.67\right| \end{gathered}$$

13.  Write each statement in terms of inequalities.

(a) y is negative.

(b) z is greater than 7.

(c) b is at most 1.

(d) w is positive and is less than or equal to 16.

(e) y is at least 2 units from 𝜋.

14. Find the indicated set if given the following. (Enter your answer as a set. Enter EMPTY for the empty set.)

A = {1, 2, 3, 4, 5, 6}    B = {2, 4, 6, 8}    C = {5, 6, 7, 8, 9, 10}

(a)    A ∪ C

(b)    A ∩ C

15.   Find the indicated set if given the following.

A = {x|x ≥ −3}

B = {x|x < 4}

C = {x|−1 < x ≤ 5}

(a)     A ∩ C

(b)    A ∩ B

16.  Express the interval in terms of inequalities.  [6, 9)

17. Express the interval in terms of inequalities.  (−∞, 6)

18. Express the inequality in interval notation.  x ≤ 1

19. Express the inequality in interval notation.  x ≥ −5

20.  Express the inequality in interval notation.  −6 < x < 4

21. Graph the set.  [−2, 7) ∪ [0, 9)

22.  Evaluate each expression.

A.

B.

23.  Evaluate each expression.

A.

B.

24.  Find the distance between the given numbers. (Simplify your answers completely.)

(a)    3 and 12

(b)    −7 and 19

(c)