Deck 2: Equations and Inequalities

Question 1

Name the indicated property.
If x = -5, then x + 2 = -5 + 2

A)reflexive property
B)transitive property
C)symmetric property
D)addition property

Answer 1

addition property

Question 2

Give the degree of the term.

- $5 x$

A)0
B)5
C)1
D)-1

Answer 2

1

Question 3

Give the degree of the term.

- $8 x ^ { 7 } b ^ { 8 } c ^ { 6 }$

A)21
B)14
C)8
D)6

Answer 3

21

Question 4

Give the degree of the term.

- $4 w ^ { 8 } c ^ { 2 }$

A)4
B)10
C)2
D)14

Question 5

Name the indicated property.
If 5x = -9, then -4(5x)= -4(-9)

A)symmetric property
B)multiplication property
C)transitive property
D)reflexive property

Question 6

Give the degree of the term.
9

A)-9
B)9
C)0
D)1

Question 7

Give the degree of the term.

- $14 x ^ { 2 } y$

A)3
B)2
C)7
D)14

Question 8

Name the indicated property.

- $$4 x = 25 , \text { then } \frac { 1 } { 4 } ( 4 x ) = \frac { 1 } { 4 } ( 25 )$$

A)reflexive property
B)multiplication property
C)symmetric property
D)transitive property

Question 9

Simplify the expression. If the expression cannot be simplified, so state.

- $- 10 y - 8 x - 2 x$

A) $- 10 y - 10 x$
B) $- 20 x y$
C) $- 10 y - 6 x$
D) $- 10 y + 6 x$

Question 10

Give the degree of the term.
-9

A)1
B)-9
C)0
D)9

Question 11

Name the indicated property.
If x = 1 and 1 = y, then x = y.

A)symmetric property
B)multiplication property
C)reflexive property
D)transitive property

Question 12

Name the indicated property.
5x + 24 = 5x + 24

A)reflexive property
B)addition property
C)symmetric property
D)transitive property

Question 13

Name the indicated property.
If x + 9 = y + 5, and y + 5 = z, then x + 9 = z

A)symmetric property
B)addition property
C)transitive property
D)reflexive property

Question 14

Simplify the expression. If the expression cannot be simplified, so state.

- $6 a - 3 a + 3$

A)3a + 3
B)-3a + 3
C)9a + 3
D)cannot be simplified

Question 15

Give the degree of the term.

- $- 5 x y$

A)0
B)1
C)-5
D)2

Question 16

Name the indicated property.
If x = 4 , then x - 4 = 4 - 4

A)addition property
B)symmetric property
C)reflexive property
D)transitive property

Question 17

Give the degree of the term.

- $3 x y ^ { 3 } z ^ { 5 }$

A)3
B)9
C)15
D)8

Question 18

Name the indicated property.
If x = -5, then -5 = x.

A)reflexive property
B)symmetric property
C)transitive property
D)multiplication property

Question 19

Name the indicated property.
If x + 2 = -7, then x + 2 - 2 = -7 - 2

A)addition property
B)symmetric property
C)reflexive property
D)transitive property

Question 20

Give the degree of the term.

- $- 7 x ^ { 4 }$

A)28
B)-7
C)-28
D)4

Question 21

Simplify the expression. If the expression cannot be simplified, so state.

- $( 8 z + 3 ) - ( 4 z - 2 )$

A) $4 z + 5$
B) $4 z - 5$
C) $12 z + 5$
D) $4 z + 1$

Question 22

Simplify the expression. If the expression cannot be simplified, so state.

- $- 5 ( 9 r + 6 ) + 7 ( 8 r + 8 )$

A)11r + 26
B)11r + 6
C)-75r
D)4r + 1

Question 23

Simplify the expression. If the expression cannot be simplified, so state.

- $6 y + 6 - 3 y + 2$

A)11y
B) $9 y + 8$
C) $3 y + 8$
D) $3 y + 4$

Question 24

Simplify the expression. If the expression cannot be simplified, so state.

- $5.8 \mathrm { k } - 1.7 - 3.5 \mathrm { k } + 9 + 2.9 \mathrm { k }$

A)12.2k + 7.3
B)5.2k + 10.7
C)5.2k - 7.3
D)5.2k + 7.3

Question 25

Simplify the expression. If the expression cannot be simplified, so state.

- $r ^ { 2 } s + 5 r s - \left[ - \left( r s + 6 r ^ { 2 } s \right) + r s \right]$

A) $12 r ^ { 3 } s ^ { 2 }$
B) $6 r ^ { 2 } s + 3 r s$
C) $- 5 r ^ { 2 } s + 7 r s$
D) $7 \mathrm { r } ^ { 2 } \mathrm {~s} + 5 \mathrm { rs }$

Question 26

Solve the equation.

-8x - (6x - 1)= 2

A) $\frac { 1 } { 14 }$
B) $- \frac { 1 } { 2 }$
C) $- \frac { 1 } { 14 }$
D) $\frac { 1 } { 2 }$

Question 27

Simplify the expression. If the expression cannot be simplified, so state.

- $1.5 x ^ { 4 } + 1.3 x ^ { 4 } + 1.5 x ^ { 4 }$

A) $5.8 x ^ { 4 }$
B) $13 x ^ { 4 }$
C) $4.3 x ^ { 4 }$
D)cannot be simplified

Question 28

Simplify the expression. If the expression cannot be simplified, so state.

- $7 \left\{ 9 y ^ { 2 } + 4 \left[ 5 y ^ { 2 } - \left( y + z ^ { 2 } \right) \right] \right\}$

A) $175 y ^ { 2 } - 28 y$
B) $83 y ^ { 2 } - 4 y - 4 z ^ { 2 }$
C) $203 y ^ { 2 } - 7 y + 7 z ^ { 2 }$
D) $203 y ^ { 2 } - 28 y - 28 z ^ { 2 }$

Question 29

Solve the equation.

-5y - 4 = 1 - 6y

A) $- \frac { 11 } { 5 }$
B) $\frac { 11 } { 5 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 5 } { 11 }$

Question 30

Solve the equation.

- $2 n - 3 = 13$

A)14
B)18
C)9
D)8

Question 31

Simplify the expression. If the expression cannot be simplified, so state.

- $- 6 ( 2 x - 7 ) - 4 x + 6$

A)8x + 48
B)-16x + 48
C)16x + 48
D)-16x - 36

Question 32

Simplify the expression. If the expression cannot be simplified, so state.

- $- 5 \left[ 8 x ^ { 2 } + 9 ( - 4 - x ) \right]$

A) $- 40 x ^ { 2 } - 45 x + 180$
B) $- 40 x ^ { 2 } + 5 x + 180$
C) $- 40 x ^ { 2 } + 45 x + 180$
D) $- 40 x ^ { 2 } - 9 x - 36$

Question 33

Simplify the expression. If the expression cannot be simplified, so state.

- $- 14 y ^ { 8 } - 5 y ^ { 8 }$

A) $- 19 y ^ { 8 }$
B) $- 19 y^{ 16}$
C) $- 9 y ^ { 8 }$
D)cannot be simplified

Question 34

Simplify the expression. If the expression cannot be simplified, so state.

- $2 x ^ { 4 } y ^ { 3 } + 2 \left( 2 x ^ { 4 } y ^ { 3 } - 9 x ^ { 3 } y ^ { 4 } \right)$

A) $6 x ^ { 4 } y ^ { 3 } - 18 x ^ { 3 } y ^ { 4 }$
B) $6 x ^ { 4 } y ^ { 3 } - 9 x ^ { 3 } y ^ { 4 }$
C) $- 12 x ^ { 7 } y ^ { 7 }$
D)cannot be simplified

Question 35

Simplify the expression. If the expression cannot be simplified, so state.

- $9 ( y + 6 ) - 4$

A)15y - 4
B) $9 y + 18$
C) $9 y + 50$
D) $9 y + 2$

Question 36

Simplify the expression. If the expression cannot be simplified, so state.

- $\left[ - 10 x ^ { 2 } + \left( 3 x ^ { 2 } + 6 \right) \right] + \left[ \left( 9 x ^ { 2 } + \left( 9 + 10 x ^ { 2 } \right) \right) - 2 x ^ { 2 } \right]$

A) $10 x ^ { 2 } + 15$
B) $- 16 x ^ { 2 } - 15$
C) $- 24 x ^ { 2 } - 3$
D) $- 28 x ^ { 2 } - 3$

Question 37

Simplify the expression. If the expression cannot be simplified, so state.

- $- 7 x ^ { 6 } - 2 x ^ { 6 }$

A) $- 9 x ^ { 6 }$
B) $- 10 x ^ { 6 }$
C) $- 9 x ^ { 12 }$
D) $- 9 x ^ { 36 }$

Question 38

Simplify the expression. If the expression cannot be simplified, so state.

- $4 + 2 ( 12 - 8 m )$

A)24 - 16m
B)28 + 16m
C)28 - 16m
D)28 - 8m

Question 39

Simplify the expression. If the expression cannot be simplified, so state.

--8y + 1 - 4 + 7 + y - 4

A)-7y
B)-9y
C) $- 9 y + 1$
D) $- 7 y - 1$

Question 40

Simplify the expression. If the expression cannot be simplified, so state.

- $- 9 y - 4 y ^ { 2 }$

A)-5y
B) $- 13 y ^ { 2 }$
C)-13y
D)cannot be simplified

Question 41

Solve the equation.

- $\frac { 1 } { 5 } ( a - 1 ) = - 3$

A)14
B)-16
C)-14
D)16

Question 42

Solve the equation.

- $1.1 x + 4.1 = 0.3 x + 0.74$

A)0.238
B)-4.158
C)-4.19
D)-4.2

Question 43

Solve the equation.

- $\frac { 1 } { 16 } b - 10 = - 4$

A)-96
B)-98
C)98
D)96

Question 44

Solve the equation.

- $\frac { 3 } { 5 } ( y - 2 ) = 1 - 3 y$

A) $\frac { 11 } { 6 }$
B) $\frac { 7 } { 6 }$
C) $\frac { 11 } { 18 }$
D) $- \frac { 11 } { 18 }$

Question 45

Solve the equation.

- $- \{ 5 ( d + 2 ) - 6 [ 3 d - 2 ( 3 d + 8 ) ] - 7 \} = - 18 d + 51$

A) $\frac { 35 } { 8 }$
B)35
C)-30
D) $\frac { 150 } { 41 }$

Question 46

Solve the equation.

- $\frac { f } { 4 } - 5 = 1$

A)-24
B)16
C)-16
D)24

Question 47

Solve the equation.

- $0.80 x - 0.40 ( 40 + x ) = 0.20 ( 40 )$

A)70
B)30
C)60
D)50

Question 48

Solve the equation.
23.9 = -22.4 - n

A)46.3
B)-1.5
C)-46.3
D)1.5

Question 49

Solve the equation.

- $2 \{ 5 - [ 5 ( k + 2 ) - 4 ( k + 2 ) ] \} = - 3 k$

A)- 1
B)- 4
C)- 6
D) $- \frac { 1 } { 2 }$

Question 50

Solve the equation.

- $- 0.05 y + 0.13 ( 1000 - y ) = 0.07 y$

A)520
B)1040
C)325
D)32.5

Question 51

Solve the equation.

- $7 ( x + 6 ) - ( 6 x - 9 ) = - 6$

A)45
B)57
C)-57
D)21

Question 52

Solve the equation.

- $8 y + 4 ( 4 + y ) = 3 ( y - 1 ) + 10 y$

A)19
B)5
C)-5
D)-19

Question 53

Solve the equation.

- $\frac { 4 } { 3 } ( 7 - x ) = x$

A) $\frac { 28 } { 5 }$
B)7
C)4
D)-4

Question 54

Solve the equation.

- $\frac { 1 } { 3 } ( r + 6 ) = \frac { 1 } { 6 } ( r + 8 )$

A)4
B)6
C)36
D)-4

Question 55

Solve the equation.

- $6 [ - 3 x - 6 - 5 ( x + 1 ) ] = 6 x - 5$

A) $- \frac { 61 } { 54 }$
B) $\frac { 11 } { 54 }$
C) $- \frac { 61 } { 3 }$
D) $\frac { 11 } { 3 }$

Question 56

Solve the equation.

- $4 ( 2 x - 3 ) = 7 ( x + 2 )$

A)26
B)2
C)-2
D)6

Question 57

Solve the equation.

- $- 6 x + 2 ( 3 x - 5 ) = - 7 - 3 x$

A)-1
B) $- \frac { 17 } { 3 }$
C)1
D) $\frac { 17 } { 3 }$

Question 58

Solve the equation.

- $0.4 ( 11 x - 6000 ) = - 0.6 ( 20 x + 4000 ) + 19.3 x$

A)1
B)-827.59
C)0.34482759
D)0

Question 59

Solve the equation.

- $\frac { 2 } { 5 } x - \frac { 1 } { 3 } x = 2$

A)-60
B)60
C)30
D)-30

Question 60

Solve the equation.

- $3 ( x + 2 ) = 4 ( x - 7 )$

A)-34
B)-22
C)22
D)34

Question 61

Solve the problem.
The average price (in dollars)to rent a studio in a certain city can be approximated by the equation p = 35.9t + 599 where t is the number of years since 1990. Solve this equation for t and use the new equation to
Determine approximately what year it will be when the average price of a studio in this city reaches $1532.40.

A)2018
B)2016
C)2019
D)2017

Question 62

Indicate whether the equation is conditional, an identity, or a contradiction.

- $2 x + 6 x = 7 x$

A)identity
B)conditional
C)contradiction

Question 63

Solve the problem.
A solution is being heated in a controlled lab environment. The temperature of the solution is estimated by the equation T = 2x + 7 where T is the temperature of the solution and x is the time in minutes starting with when
The solution was subjected to the heat. What will be the temperature of the solution when x = 5 minutes?

A)3
B)17
C)9
D)45

Question 64

Indicate whether the equation is conditional, an identity, or a contradiction.

- $2 x = 2 x$

A)conditional
B)contradiction
C)identity

Question 65

Evaluate the formula for the values given.

- $$L = \frac { P - 2 W } { 2 } \text { when } P = 20 \text { and } W = 3$$

A)L = 8.5
B)L = 10
C)L = 7
D)L = 17

Question 66

Solve the problem.

-A canvas for a mural is in the shape of a right triangle. Before the mural can be painted, the canvas must be varnished. The base of the mural is 3 meters and the height of the mural is 11 meters. How many cans of varnish
Will you need if each can covers 10 square meters? The formula for the area of a right triangle is A $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh } .$

A)17 cans of varnish
B)2 cans of varnish
C)4 cans of varnish
D)7 cans of varnish

Question 67

Solve the problem.
Josh makes a $2500, 4% simple interest personal loan to his friend Sean for a period of 7 years. When Sean settles his loan at the end of the 7 years, how much money, in total, must he pay Josh? The formula for simple
Interest is I = prt.

A)$700
B)$72,500
C)$2528
D)$3200

Question 68

Solve the equation for the specified symbol.

- $\Delta = \frac { \varrho ( \odot ) } { \alpha } + \square \text { for } \odot$

A) $\odot = \frac { \alpha } { \Delta - \square }$
B) $\odot = \frac { \mathrm { Q } ( \Delta - \square ) } { \alpha }$
C) $\odot = \frac { \Delta - \square } { \varrho }$
D) $\odot = \frac { \alpha ( \Delta - \square) } { \varrho }$

Question 69

Indicate whether the equation is conditional, an identity, or a contradiction.

- $6 x + 18 = 6 ( x + 3 ) + 8$

A)contradiction
B)conditional
C)identity

Question 70

Indicate whether the equation is conditional, an identity, or a contradiction.

- $4 ( 2 x - 6 ) = 8 x - 24$

A)conditional
B)contradiction
C)identity

Question 71

Evaluate the formula for the values given.

- $$\mathrm { d } = \text { rt } \text { when } r = 9 \text { and } t = 9$$

A)d = 90
B)d = 81
C)d = 0.1
D)d = 72

Question 72

Solve the problem.

-Find the amount in a savings account at the end of 4 years if the amount originally deposited (the principal)is $5000 and the interest rate is 6.5% compounded quarterly.
The formula for the final amount isal amount is $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$

A)$6471.11
B)$5333.01
C)$7118.22
D)$81,300.00

Question 73

Evaluate the formula for the values given.

- $$P = 2 L + 2 W \text { when } L = 3 \text { and } W = 5$$

A)P = 11
B)P = 30
C)P = 8
D)P = 16

Question 74

Solve the problem.

-In Little City Park there is a circular fountain. The park district has decided to plant a circular garden around the fountain. In order to purchase the appropriate number of plants, they must determine the area of the garden
In square feet. Find the area rounded to two decimal places, if necessary. The formula for the area of a circle is $\mathrm { A } = \pi \mathrm { r } ^ { 2 } . \text { Use } 3.14$ 4 a s an approximation for ?.

A)1570 sq ft
B)3140 sq ft
C)785 sq ft
D)2464.9 sq ft

Question 75

Solve the problem.

-Mr. Brown just fenced in an area for his dog. He used exactly 40 feet of fencing for the rectangular shaped enclosure. If the length of the enclosure is 14 feet, what is its width? The formula for the perimeter of a rectangle
Iss P $P = 21 + 2 w$

A)6 ft
B)34 ft
C) $2 \frac { 6 } { 7 } \mathrm { ft }$
D)12 ft

Question 76

Solve the problem.
Find the total cost of tiling a rectangular floor that is 5 meters long and 10 meters wide if it costs $8.96 to tile one square meter. Round to the nearest cent. The formula for the area of a rectangle is A = lw.

A)$50.00
B)$268.80
C)$134.40
D)$448.00

Question 77

Evaluate the formula for the values given.

- $$B = \frac { 3 V } { h } \text { when } V = 12 \text { and } h = 6$$

A)B = 72
B)B = 2
C)B = 6
D)B = 18

Question 78

Solve the problem.
A family is preparing an area in their yard for playground equipment. They have marked an area that is 15 feet by 24 feet. They want to fill the area with wood chips to a depth of 6 inches. Find the volume of wood chips
Required in cubic feet.

A)2160 cubic ft
B)90 cubic ft
C)180 cubic ft
D)720 cubic ft

Question 79

Evaluate the formula for the values given.

- $$A = \frac { 1 } { 2 } b h \text { when } b = 8 \text { and } h = 6$$

A)A = 14
B)A = 48
C) $\mathrm { A } = 14 \frac { 1 } { 2 }$
D)A = 24

Question 80

Solve the equation for the specified symbol.

- $\mathrm { V } = \frac { \mathrm { B } \odot } { \mathrm { q } } \text { for } \odot$

A) $\odot = \frac { q B } { V }$
B) $\odot = \frac { \mathrm { V } } { \mathrm { qB } }$
C) $\odot = \frac { q V } { B }$
D) $\odot = \frac { B } { q V }$