Chapter 1 — Preliminary Information

Exercise 1-3: Variables and Expressions

Problems

Q1

Is $\sqrt{9}$ an integer?

Q2

Is $-\frac{4}{7}$ a real number?

Q3

Commute the 3 and the $x$: $2y + 3 + x$

Q4

Associate the $4a$ and the $2c$: $4a + 2c + 5d$

Q5

Distribute the 5: $5(3x - 7)$

Q6

Write the additive inverse of $\frac{5}{8}$.

Q7

Write the multiplicative identity element.

Q8

If $3x$ equals 42, what does $x$ equal?

Q9

Multiply: $(2.3)(4)$

Q10

Divide and simplify: $\left(\frac{2}{3}\right) \div \left(\frac{6}{7}\right)$

1

Carry out the indicated operations in the agreed-upon order: $5 + 6 \times 7$

2

Carry out the indicated operations in the agreed-upon order: $3 + 8 \times 7$

3

Carry out the indicated operations in the agreed-upon order: $9 - 4 + 5$

4

Carry out the indicated operations in the agreed-upon order: $11 - 6 + 4$

5

Carry out the indicated operations in the agreed-upon order: $12 \div 3 \times 2$

6

Carry out the indicated operations in the agreed-upon order: $18 \div 9 \times 2$

7

Carry out the indicated operations in the agreed-upon order: $7 - 8 \div 2 + 4$

8

Carry out the indicated operations in the agreed-upon order: $24 - 12 \times 2 + 4$

9

Carry out the indicated operations in the agreed-upon order: $16 - 4 + 12 \div 6 \times 2$

10

Carry out the indicated operations in the agreed-upon order: $50 - 30 \times 2 + 8 \div 2$

11

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $4x - 1$

12

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $3x - 5$

13

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $|3x - 5|$

14

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $|4x - 1|$

15

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $5 - 7x - 8$

16

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $8 - 5x - 2$

17

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $|8 - 5x| - 2$

18

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $|5 - 7x| - 8$

19

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $x^2 - 4x + 6$

20

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $x^2 + 6x - 9$

21

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $4x^2 - 5x - 11$

22

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $5x^2 - 7x + 1$

23

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $5 - 2 \cdot x$

24

Evaluate the given expression (a) for $x = 2$, (b) for $x = -3$: $3 + 4 \cdot x$

25

Simplify the given expression: $6 - [5 - (3 - x)]$

26

Simplify the given expression: $2x - [3x + (x - 2)]$

27

Simplify the given expression: $7(x - 2(3 - x))$

28

Simplify the given expression: $3(6x - 5(x - 1))$

29

Simplify the given expression: $7 - 2[3 - 2(x + 4)]$

30

Simplify the given expression: $8 + 4[5 - 6(x - 2)]$

31

Simplify the given expression: $3x - [2x + (x - 5)]$

32

Simplify the given expression: $4x - [3x - (2x - x)]$

33

Simplify the given expression: $6 - 2[x - 3 - (x + 4) + 3(x - 2)]$

34

Simplify the given expression: $7[2 - 3(x - 4) + 4(x - 6)]$

35

Simplify the given expression: $6[x - \tfrac{1}{2}(x - 1)]$

36

Simplify the given expression: $8[2x - \tfrac{1}{4}(6x + 5)]$

37

Simplify the given expression: $x^2 + y^2 - [x(x + y) - y(y - x)]$

38

Simplify the given expression: $4x^2 - 2x(x - 2y) + 2y(2y + x) - 2x^2$

39

Simplify the given expression: $-(-(-(-x)))$

40

Simplify the given expression: $x - [x - (x - \overline{x - y})]$

41

Calvin Butterball and Phoebe Small evaluate the expression $|x - 3|$ for $x = 7$, getting:

Calvin: $|x - 3| = |7 - 3| = 7 + 3 = \underline{\underline{10}}$

Phoebe: $|x - 3| = |7 - 3| = |4| = \underline{\underline{4}}$

Who is right? What mistake did the other one make?

42

Kay Oss evaluates the expression $|x + 2| - 5x$ by substituting 7 for the first $x$ and 3 for the second $x$. What axiom did Kay violate?

Solutions

1

Answer: 47

3

Answer: 10

5

Answer: 8

7

Answer: 7

9

Answer: 16

11

Answer: a. 7 b. $-13$

13

Answer: a. 1 b. 14

15

Answer: a. $-17$ b. 18

17

Answer: a. 0 b. 21

19

Answer: a. 2 b. 27

21

Answer: a. $-5$ b. 40

23

Answer: a. 1 b. 11

25

Answer: $4 - x$

27

Answer: $21x - 42$

29

Answer: $4x + 17$

31

Answer: 5

33

Answer: $32 - 6x$

35

Answer: $3x + 3$

37

Answer: $2y^2 - 2xy$

39

Answer: $x$

41

Answer: Phoebe