Deck 2: Linear and Absolute Value Equations and Inequalities

Question 1

Build a variable expression for the given phrase

-Six times a number

A) $6-x$
B) $6+x$
C) $\frac{6}{x}$
D) $6 \mathrm{x}$

Answer 1

$6 \mathrm{x}$

Question 2

Build a variable expression for the given phrase

-A number decreased by two

A) $2-\mathrm{x}$
B) $\frac{x}{2}$
C) $x+2$
D) $x-2$

Answer 2

$x-2$

Question 3

Build a variable expression for the given phrase

-The sum of a number and three hundred fifty- eight

A) $\frac{x}{358}$
B) $x+358$
C) $358 x$
D) $358-\mathrm{x}$

Answer 3

$x+358$

Question 4

Build a variable expression for the given phrase

-A number minus five hundred five

A) $505 x$
B) $x+505$
C) $505-\mathrm{x}$
D) $x-505$

Question 5

Build a variable expression for the given phrase

-Four divided by a number

A) $\frac{x}{4}$
B) $\frac{1}{4 \mathrm{x}}$
C) $4-x$
D) $\frac{4}{\mathrm{x}}$

Question 6

Build a variable expression for the given phrase

-The difference between three times a number and eight

A) $3-x+8$
B) $3 x-8$
C) $8-3 x$
D) $3(x-8)$

Question 7

Build a variable expression for the given phrase

-The product of eight and three more than a number

A) $8+3 \cdot x$
B) $8(x+3)$
C) $8 \cdot 3+x$
D) $(8+3) \mathrm{x}$

Question 8

Build a variable expression for the given phrase

-Two times the difference of two numbers.

A) $2 \mathrm{x}-\mathrm{y}$
B) $x-2 y$
C) $2(x \div y)$
D) $2(x-y)$

Question 9

Build a variable expression for the given phrase

-Two times a number, increased by 21

A) $2(x+21)$
B) $2 \cdot 21+\mathrm{x}$
C) $2 x+21$
D) $2 \mathrm{x}$

Question 10

Build a variable expression for the given phrase

-Three less than 21 times a number

A) $21(\mathrm{x}-3)$
B) 3 - 21x
C) $21 x-3$
D) $21-3 x$

Question 11

A lawyer charges $\$ 276$ per hour to take a case. If we let $h$ represent the number of hours she works on the case, build a variable expression for the amount she would charge for the case.

A) $276+h$
B) $276 \div \mathrm{h}$
C) $276 \mathrm{~h}$
D) $\mathrm{h} \div 276$

Question 12

A college charges $\$ 219$ per unit for tuition. If we let $u$ represent the number of units that a student is taking, build a variable expression for the student's tuition.

A) $219 \div \mathrm{u}$
B) $219 u$
C) $u \div 219$
D) $219+u$

Question 13

A realtor has a base salary of $\$ 83,500$ per year plus $\$ 1500$ per house sold. If we let $h$ represent the number of houses she sells in a year, build a variable expression for the total amount of money she will make that year.

A) $83,500 \mathrm{~h}+1500$
B) $83,500+1500 \mathrm{~h}$
C) $(83,500+1500) \mathrm{h}$
D) $83,500+1500+h$

Question 14

A lawyer charges $\$ 565$ per day plus expenses to take a case. If we let $d$ represent the number of days that the lawyer works on the case, and if he has $\$ 1550$ in expenses, build a variable expression for the amount of money he would charge for the case.

A) $(565+1550) d$
B) $565 \mathrm{~d}+1550 \mathrm{~d}$
C) $565 \mathrm{~d}+1550$
D) $565+1550 \mathrm{~d}$

Question 15

Write the given expression using words.

- $x-2$

A) Two more than a number
B) Two less than a number
C) Two added to a number
D) Two times a number

Question 16

Write the given expression using words.

- $9 \mathrm{x}$

A) Nine less than a number
B) Nine more than a number
C) Nine times a number
D) Nine divided by a number

Question 17

Write the given expression using words.

- $5 x+12$

A) Five more than twelve times a number
B) Twelve more than five times a number
C) Five less than twelve times a number
D) Twelve less than five times a number

Question 18

Write the given expression using words.

- $2 \mathrm{x}-3$

A) Three less than twice a number
B) Two more than three times a number
C) Two less than three times a number
D) Three more than twice a number

Question 19

Evaluate the algebraic expression under the given conditions

- $7 \mathrm{x}+9$ for $\mathrm{x}=9$

A) 54
B) 72
C) 126
D) 16

Question 20

Evaluate the algebraic expression under the given conditions

- $-5 x+2$ for $x=7$

A) -37
B) -3
C) -70
D) - 33

Question 21

Evaluate the algebraic expression under the given conditions

- $8-2 y$ for $y=-3$

A) 11
B) 2
C) 14
D) 10

Question 22

Evaluate the algebraic expression under the given conditions

- $7(6-x)$ for $x=3$

A) 4
B) 39
C) 21
D) 10

Question 23

Evaluate the algebraic expression under the given conditions

- $(x-3)(3 x-3)$ for $x=-3$

A) 51
B) -72
C) 33
D) 72

Question 24

Evaluate the algebraic expression under the given conditions

- $y^{2}-5 y-12$ for $y=2$

A) -14
B) 2
C) -30
D) - 18

Question 25

Evaluate the algebraic expression under the given conditions

- $-2 x^{2}+4 x+7$ for $x=-4$

A) -1
B) -45
C) -51
D) - 41

Question 26

Evaluate the algebraic expression under the given conditions

- $17-m^{2}$ for $m=9$

A) 64
B) -64
C) 98
D) 676

Question 27

Evaluate the algebraic expression under the given conditions

- $x^{5}-20 x^{4}-252 x^{3}-727$ for $x=0$

A) -727
B) -998
C) 0
D) -999

Question 28

Evaluate the algebraic expression under the given conditions

- $\mathrm{a}^{3}+4 \mathrm{a}-18$ for $\mathrm{a}=5$

A) 87
B) 127
C) 55
D) 627

Question 29

Evaluate the algebraic expression under the given conditions

- $9 x+2 y$ for $x=4, y=8$

A) 44
B) 88
C) 80
D) 52

Question 30

Evaluate the algebraic expression under the given conditions

- $-4 x-3 y$ for $x=-9, y=7$

A) 15
B) -49
C) -1
D) 63

Question 31

Evaluate the algebraic expression under the given conditions

- $3(8 x+3 y)$ for $x=3, y=-5$

A) -21
B) -93
C) 99
D) 27

Question 32

Evaluate the algebraic expression under the given conditions

- $b^{2}$ - 4ac for $b=-4, a=4, c=6$

A) - 80
B) - 86
C) -76
D) - 90

Question 33

Evaluate the algebraic expression under the given conditions

- $\mathrm{b}^{2}$ - 4ac for $\mathrm{a}=8, \mathrm{~b}=-8$ , and $\mathrm{c}=-6$

A) 256
B) 128
C) -2880
D) 108

Question 34

Evaluate the algebraic expression under the given conditions

- $6(x+h)+7$ for $x=6$ and $h=0.001$

A) 42.994
B) 29.006
C) 43.006
D) 43.001

Question 35

Evaluate the algebraic expression under the given conditions

- $(\mathrm{x}+\mathrm{h})^{2}-4(\mathrm{x}+\mathrm{h})+8$ for $\mathrm{x}=-2$ and $\mathrm{h}=1$

A) 21
B) 13
C) 18
D) 17

Question 36

If a projectile is launched straight upward from the ground with an initial velocity of v0 (in feet/second), then the height
(in feet) of the projectile after t seconds is given by the expression -16t2 + v0t. Find the height of the projectile (in feet)
that was launched with the given initial velocity after t seconds.

-150 feet/second, 7 seconds

A) 38 feet
B) 266 feet
C) 938 feet
D) 1834 feet

Question 37

If a projectile is launched straight upward from the ground with an initial velocity of v0 (in feet/second), then the height
(in feet) of the projectile after t seconds is given by the expression -16t2 + v0t. Find the height of the projectile (in feet)
that was launched with the given initial velocity after t seconds.

-63.2 feet/second, 2 seconds

A) 94.4 feet
B) 190.4 feet
C) 62.4 feet
D) 31.2 feet

Question 38

If a projectile is launched straight upward from the ground with an initial velocity of v0 (in feet/second), then the height
(in feet) of the projectile after t seconds is given by the expression -16t2 + v0t. Find the height of the projectile (in feet)
that was launched with the given initial velocity after t seconds.

-94 feet/second, 3.1 seconds

A) 853.74 feet
B) 241.8 feet
C) 143.6 feet
D) 137.64 feet

Question 39

Simplify, where possible

- $8(x+6)$

A) $8 x+6$
B) $48 x$
C) $x+48$
D) $8 x+48$

Question 40

Simplify, where possible

- $5(x-7)$

A) $-35 x$
B) $5 x+35$
C) $5 x-35$
D) $5 \mathrm{x}-7$

Question 41

Simplify, where possible

- $8(1-y)$

A) $8-y$
B) $8+8 y$
C) $8-8 y$
D) 1 - $8 y$

Question 42

Simplify, where possible

- $2(9 m+6)$

A) $18 \mathrm{~m}+12$
B) $108 \mathrm{~m}$
C) $18 \mathrm{~m}+6$
D) $9 m+12$

Question 43

Simplify, where possible

- $7(7 a-4)$

A) $49 a-4$
B) $49 a-28$
C) $7 \mathrm{a}-28$
D) - 196a

Question 44

Simplify, where possible

- $2(8-8 y)$

A) - 128y
B) 16 - $16 y$
C) 8 - 16y
D) $16-8 y$

Question 45

Simplify, where possible

- $2(x+7+8 y)$

A) $2 x+14+16 y$
B) $2 x+14+8 y$
C) $x+14+16 y$
D) $2 x+7+8 y$

Question 46

Simplify, where possible

- $-(3 x-2)$

A) $-3 x+2$
B) $6 x$
C) $-3 x-2$
D) $3 \mathrm{x}-2$

Question 47

Simplify, where possible

- $-3(5 m-2)$

A) $-15 m+6$
B) $-15 m-6$
C) $6 \mathrm{~m}-15$
D) $-15 m-2$

Question 48

Simplify, where possible

- $-2(-3 x-6 y+8)$

A) $6 x-12 y+16$
B) $6 x-6 y+8$
C) $6 x+12 y-16$
D) $6 x+6 y-8$

Question 49

Simplify, where possible

- $6 x+12 x$

A) $18 x$
B) $36 x$
C) $18 x^{2}$
D) $72 x$

Question 50

Simplify, where possible

- $10 x-6 x$

A) $4 x$
B) $-4 x$
C) $4 x^{2}$
D) $16 x$

Question 51

Simplify, where possible

- $-3 b+7 b$

A) $4 b^{2}$
B) $-10 b$
C) $-4 b$
D) $4 \mathrm{~b}$

Question 52

Simplify, where possible

- $8 \mathrm{a}-3 \mathrm{a}+5$

A) $5 a+5$
B) $-5 a+5$
C) $11 a+5$
D) $10 \mathrm{a}$

Question 53

Simplify, where possible

- $6 a-4 b+2$

A) $2 a b+2$
B) $-2 a+2$
C) $4 \mathrm{ab}$
D) $6 a-4 b+2$

Question 54

Simplify, where possible

- $7 \mathrm{x}+10-10 \mathrm{x}-9$

A) $-3 x+1$
B) $3 x+1$
C) $17 x+19$
D) $-3 x+10 y-9$

Question 55

Simplify, where possible

- $30 x-9 y-20 x-7 y$

A) $10 x-9 y-7$
B) $10 x-2 y$
C) $10 x-16 y$
D) - $10 x-16 y$

Question 56

Simplify, where possible

- $21 m-8-4 m-5$

A) $17 \mathrm{~m}-3$
B) $17 m-8 n-5$
C) $17 \mathrm{~m}-13$
D) $-17 m-13$

Question 57

Simplify, where possible

- $13 x-6 y-29 x+2 y$

A) $-16 x-4 y$
B) $-16 x-6 y+2$
C) $16 x-4 y$
D) $-16 x-8 y$

Question 58

Simplify, where possible

- $19 x-9 y+10-11 x-6-6 y$

A) $8 x-3 y+4$
B) $8 x-15 y+4$
C) $-8 x-15 y+4$
D) $-8 x-3 y+4$

Question 59

Simplify, where possible

- $2 y-4(x+4 y)$

A) $-14 y+x$
B) $6 y-4 x$
C) $-14 y-4 x$
D) $18 y-4 x$

Question 60

Simplify, where possible

-7(4m-1) $+6 m+1$

A) $34 \mathrm{~m}-6$
B) $-22 m-6$
C) $10 \mathrm{~m}-6$
D) $34 \mathrm{~m}$

Question 61

Simplify, where possible

- $3 x-y-9(4 x-8 y)$

A) $-33 x-73 y$
B) $-33 x-9 y$
C) $-33 x+7 y$
D) $-33 x+71 y$

Question 62

Simplify, where possible

-7(3y-4z) - y

A) $20 y-4 z$
B) $20 y-28 z$
C) $-4 y-4 z$
D) $22 y-28 z$

Question 63

Simplify, where possible

- $-9(2 z-6)-1$

A) $-18 z-55$
B) $2 z+53$
C) $-18 z-7$
D) $-18 z+53$

Question 64

Simplify, where possible

- $8 y-8(6 y-2)$

A) $-40 y-16$
B) $-40 y-2$
C) $8 y+16$
D) $-40 y+16$

Question 65

Simplify, where possible

- $8 x-(4 x-6)-(-7 x+1)$

A) $11 x+7$
B) $19 x+5$
C) $11 x-7$
D) $11 x+5$

Question 66

Simplify, where possible

- $-3(2 m-5)-4(2 m+3)$

A) $-14 m-3$
B) $-14 \mathrm{~m}-2$
C) $4 \mathrm{~m}+3$
D) $-14 m+3$

Question 67

Simplify, where possible

- $9 x-y-2(6 x-5 y+9 z)$

A) $-3 x-11 y+18 z$
B) $-3 x-6 y+9 z$
C) $-3 x+4 y-9 z$
D) $-3 x+9 y-18 z$

Question 68

Simplify, where possible

- $7 y+z-6(z+9 y)$

A) $-47 y-5 z$
B) $61 y-5 z$
C) $16 y-5 z$
D) $-2 y-6 z$

Question 69

Simplify, where possible

- $2 a-2 b+6 c-2(5 a+6 b-9 c)$

A) $-8 a-8 b+15 c$
B) $-8 a+10 b-12 c$
C) $-8 a-14 b+24 c$
D) $-3 a+4 b-3 c$

Question 70

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $9 a^{2}-9 a+5$

A) a) 3
b) $9 a^{2}, 9 a, 5$
c) $9,9,5$

B) a) 2
b) $9 a^{2},-9 a$
c) $9,-9$

C) a) 3
b) $9 a^{2},-9 a, 5$
c) $9,-9,5$

D) a) 3
b) $9 a^{2},-9 a,-5$
c) $9,-9,-5$

Question 71

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $-6 y-2$

A) a) 2
b) $-6 y,-2$
c) $-6,-2$

B) a) 1
b) $-8 y$
c) -8

C) a) 2
b) $6 y, 2$
c) 6,2

D) a) 2
b) - 6y, 2
c) $-6,2$

Question 72

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $2 x^{3}-13 x^{2}+12 x-11$

A) a) 4
b) $2 x^{3},-13 x^{2}, 12 x,-11$
c) $2,-13,12,-11$

B) a) 3
b) $-11 x^{2}, 12 x,-11$
c) $-11,12,-11$

C) a) 4
b) $2 x^{3}, 13 x^{2}, 12 x, 11$
c) $2,13,12,11$

D) a) 3
b) $-11 x^{2}, 12 x, 11$
c) - 11, 12, 11

Question 73

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $22 x^{4}-7 x^{3}+12 x^{2}-11 x+201$

A) a) 4
b) $15 x^{3}, 12 x^{2},-11 x, 201$
c) $15,12,-11,201$

B) a) 5
b) $22 x^{4}, 7 x^{3}, 12 x^{2}, 11 x, 201$
c) $22,7,12,11,201$

C) a) 5
b) $22 x^{4},-7 x^{3}, 12 x^{2},-11 x, 201$
c) $22,-7,12,-11,201$

D) a) 4
b) $15 x^{3}, 12 x^{2}, 11 x, 201$
c) 15, 12, 11, 201

Question 74

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $6\left(5 x^{2}-x\right)+9 x^{2}+x$

A) a) 2
b) $-21 x^{2},-5 x$
c) - 21, - 5

B) a) 2
b) $14 x^{2},-5 x$
c) $14,-5$

C) a) 2
b) $39 x^{2},-5 x$
c) $39,-5$

D) a) 1
b) $39 x^{2}$
c) 39

Question 75

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $6 x^{2}-x-9\left(6 x^{2}-4 x+6\right)$

A) a) 3
b) $-48 x^{2},-37 x,-54$
c) $-48,-37,-54$

B) a) 3
b) $-48 x^{2},-5 x, 6$
c) $-48,-5,6$

C) a) 3
b) $-48 x^{2}, 3 x,-6$
c) $-48,3,-6$

D) a) 3
b) $-48 x^{2}, 35 x,-54$
c) $-48,35,-54$

Question 76

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $6 a-7 b+2 c-9(2 a+9 b-9 c)$

A) a) 3
b) - $12 \mathrm{a}, 74 \mathrm{~b},-79 \mathrm{c}$
c) $-12,74,-79$

B) a) 3
b) - 12a, - 16b, 11c
c) $-12,-16,11$

C) a) 3
b) - 12a, - 88b, 83c
c) $-12,-88,83$

D) a) 3
b) $4 \mathrm{a}, 2 \mathrm{~b},-7 \mathrm{c}$
c) $4,2,-7$

Question 77

For the expression,
A) determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.

- $6(-3 y+z)-(z-9 y)$

A) a) 2
b) $-12 y, 5 z$
c) $-12,5$

B) a) 2
b) $-27 y, 5 z$
c) $-27,5$

C) a) 2
b) $-9 y, 6 z$
c) $-9,6$

D) a) 2
b) $-9 y, 5 z$
c) $-9,5$

Question 78

Rewrite the expression $(7+4 a)+8 b$ by applying the associative property. If the associative property does not apply, state this.

A) $8 \mathrm{~b}+(7+4 \mathrm{a})$
B) $7+(4 a+8 b)$
C) $(4 a+7)+8 b$
D) Associative property does not apply

Question 79

Rewrite the expression ( 8 - 7a) - $6 \mathrm{~b}$ by applying the associative property. If the associative property does not apply, state this.

A) $(7 a-8)-6 b$
B) $6 \mathrm{~b}-(8-7 \mathrm{a})$
C) $8-(7 a-6 b)$
D) Associative property does not apply

Question 80

Rewrite the expression $(10 \cdot \mathrm{m}) \cdot \mathrm{n}$ by applying the associative property. If the associative property does not apply, state this.

A) $(m \cdot 10) \cdot n$
B) $10 \cdot(\mathrm{m} \cdot \mathrm{n})$
C) $\mathrm{n} \cdot(10 \cdot \mathrm{m})$
D) Associative property does not apply