Deck 9: Equations, Inequalities, and Problem Solving

Question 1

Solve the equation.
x + 1.4 = 22

A)22.9
B)20.6
C)23.4
D)20.1

Answer 1

20.6

Question 2

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
7x - 6x + 5 = 5

A)-5
B)0
C)10
D)5

Answer 2

0

Question 3

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
2x - 1 = 3(x - 7)

A)22
B)-22
C)20
D)-20

Answer 3

20

Question 4

Solve the equation.
x - 1.2 = 20.5

A)21.7
B)21.2
C)18.8
D)19.3

Question 5

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
10y = 6y + 10 + 3y

A)-100
B)10
C)100
D)-10

Question 6

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
8(y - 9)= 9y - 72

A)-72
B)72
C)-144
D)0

Question 7

Solve the equation. Don't forget to first simplify each side of the equation, if possible.

-6x = 8(3x + 8)

A) $\frac { 32 } { 3 }$
B) $- \frac { 32 } { 9 }$
C) $\frac { 32 } { 9 }$
D) $\frac { 9 } { 32 }$

Question 8

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-4a + 2 + 5a = 10 - 20

A)-32
B)32
C)-12
D)12

Question 9

Solve the equation.
-12 = b + 3

A)9
B)-15
C)15
D)-9

Question 10

Solve the equation.

- $x + \frac { 1 } { 6 } = - \frac { 1 } { 18 }$

A) $- \frac { 2 } { 9 }$
B) $- \frac { 1 } { 9 }$
C) $- \frac { 25 } { 108 }$
D) $- \frac { 1 } { 12 }$

Question 11

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-5x - 20 + 6x = 4

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

Question 12

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
3(5x + 2)- 52 = 8x - 4

A)42
B)6
C)294
D)-6

Question 13

Solve the equation.

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

A)14
B) $\frac { 14 } { 5 }$
C) $\frac { 16 } { 5 }$
D) $\frac { 2 } { 5 }$

Question 14

Solve the equation.
b + 18 = 12

A)-6
B)6
C)30
D)-30

Question 15

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-25 + 11 = 5x + 2 - 4x

A)38
B)16
C)-16
D)-38

Question 16

Solve the equation.
y - 12.8 = 7.2

A)19.5
B)5.6
C)20
D)5.1

Question 17

Solve the equation.

- $x + \frac { 1 } { 10 } = \frac { 9 } { 10 }$

A)1
B) $\frac { 8 } { 9 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 7 } { 10 }$

Question 18

Solve the equation.
t - 1 = 14

A)13
B)15
C)-15
D)-13

Question 19

Solve the equation.

- $x - \frac { 1 } { 7 } = \frac { 6 } { 7 }$

A) $\frac { 4 } { 7 }$
B)1
C) $\frac { 5 } { 6 }$
D) $\frac { 5 } { 7 }$

Question 20

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-9b + 5 + 7b = -3b + 10

A)-10
B)5
C)-5
D)10

Question 21

Solve the equation. Don't forget to first simplify each side of the equation, if possible.

- $\frac { 2 } { 3 } x + \frac { 5 } { 6 } = - \frac { 1 } { 3 } x - \frac { 1 } { 2 }$

A) $- \frac { 5 } { 8 }$
B) $- \frac { 4 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 1 } { 3 }$

Question 22

Solve the equation.

- $\frac { 1 } { 24 } a$ = 0

A)24
B)-24
C)1
D)0

Question 23

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
5(k + 1)- (4k + 9)= 7

A)11
B)- 11
C)- 15
D)3

Question 24

Solve the equation.
-4x = -24

A)20
B)-20
C)2
D)6

Question 25

Write the algebraic expression described.
In the race for Student Body President, Jose received 363 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

A)(x + 363)votes
B)(363x)votes
C)(363 - x)votes
D)(x - 363)votes

Question 26

Solve the equation.

- $\frac { \mathrm { n } } { 2 }$ = 6

A)7
B)8
C)3
D)12

Question 27

Write the algebraic expression described.
A quadrilateral is a four-sided figure whose angle sum is 360°. If one angle measures x°, a second angle measures 4x°, and a third angle measures 9x°, express the measure of the fourth angle in terms of x.

A)(360 - 14x)°
B)(360 - 13x)°
C)(14x - 360)°
D)(360 + 14x)°

Question 28

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
28(x - 1)= -4(x + 7)

A)0
B)24
C)all real numbers
D)ø

Question 29

Solve the equation.

- $- \frac { 1 } { 3 } x$ = 8

A)4
B)-3
C)5
D)-24

Question 30

Write the algebraic expression described.
Two numbers have a sum of 25. If one number is q, express the other number in terms of q.

A)q + 25
B)q - 25
C)25 - 2q
D)25 - q

Question 31

Solve the equation.
6a = -54

A)-9
B)60
C)1
D)-60

Question 32

Write the algebraic expression described.
A 31-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

A)(z + 31)cm
B)(31 - z)cm
C)(31 - 2z)cm
D)(z - 31)cm

Question 33

Solve the equation. Don't forget to first simplify each side of the equation, if possible.

-(x - 7)- (x + 8)= 2x

A)3
B) $- \frac { 15 } { 7 }$
C)- 3
D) $- \frac { 15 } { 2 }$

Question 34

Solve the equation.
-45.6 = -7.6c

A)2
B)38
C)-38
D)6

Question 35

Solve the equation. Don't forget to first simplify each side of the equation, if possible.

-3(6x - 2)= 9x - 9

A) $\frac { 5 } { 3 }$
B) $- \frac { 1 } { 9 }$
C) $- \frac { 1 } { 3 }$
D) $- - \frac { 1 } { 3 }$

Question 36

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-8.5 + 5x - 6.1 + 2x - 2.8 = 5.2 + 8x + 1.3

A)-10.9
B)-23.9
C)23.9
D)10.9

Question 37

Write the algebraic expression described.

-During a walk-a-thon, Rosilyn walked 9 fewer laps than June walked. If June walked b laps, how many laps did Rosilyn walk?

A)(9 - b)laps
B)(b - 9)laps
C) $\left( \frac { b } { 9 } \right)$ la lps
D)(b + 9)laps

Question 38

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
3(x + 6)= 4(x - 7)

A)-10
B)46
C)all real numbers
D)ø

Question 39

Write the algebraic expression described.
The sum of the angles of a triangle is 180°. If one angle of a triangle measures x° and a second angle measures (4x + 20)°, express the measure of the third angle in terms of x.

A)(200 - 5x)°
B)(160 - 4x)°
C)(160 - 5x)°
D)(160 + 5x)°

Question 40

Solve the equation.

- $- \frac { 3 } { 4 } \mathrm {~d} = \frac { 4 } { 9 }$

A) $\frac { 32 } { 9 }$
B) $- \frac { 27 } { 16 }$
C) $- \frac { 16 } { 27 }$
D) $\frac { 16 } { 27 }$

Question 41

Write the algebraic expression described.
If x is the first of three consecutive integers, express the sum of 36 and the third integer as an algebraic expression in terms of x.

A)x + 38
B)x + 36
C)2x + 38
D)x + 37

Question 42

Solve the equation.
0.4x - 0.9x - 5 = 20

A)48
B)-50
C)50
D)-48

Question 43

Solve the equation.

- $\frac { x } { 7 } + 4 = 9$

A)93
B)35
C)12
D)91

Question 44

Solve the equation.
-z = 7

A)-1
B)-7
C)7
D)0

Question 45

Write the algebraic expression described.
If x represents the first of three consecutive even integers, express the sum of the three integers in terms of x.

A)3x + 12
B)3x + 6
C)3x + 3
D)x + 6

Question 46

Solve the equation.

- $\frac { 2 } { 7 } \mathrm { k } = \frac { 4 } { 7 }$

A)17
B)18
C)2
D)3

Question 47

Solve the equation.
4x - x = 4 - 25

A)-7
B)7
C)-3
D)3

Question 48

Solve the equation.

-5x - (4x - 1)= 2

A)- 1
B) $\frac { 1 } { 9 }$
C) $- \frac { 1 } { 9 }$
D)1

Question 49

Solve the equation.
9x - 14x = -17 - 13

A)6
B)5
C)-6
D)-5

Question 50

Solve the equation.

-(y - 3)- (y + 9)= 4y

A)- 4
B)- 12
C) $\frac { 5 } { 4 }$
D)- 3

Question 51

Solve the equation.

- $\frac { 1 } { 4 } a - \frac { 1 } { 4 } = - 3$

A)-11
B)-13
C)11
D)13

Question 52

Solve the equation.

-5(2x - 1)= 20

A) $\frac { 19 } { 10 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 21 } { 10 }$

Question 53

Solve the equation.

- $\frac { 1 } { 4 } \mathrm { f }$ - 3 = 1

A)-8
B)8
C)16
D)-16

Question 54

Solve the equation.
-19 = 3x - 10

A)3
B)-3
C)-8
D)-12

Question 55

Solve the equation.

-8x - 9x - 9 = 6x

A) $- \frac { 9 } { 7 }$
B) $\frac { 7 } { 9 }$
C) $\frac { 9 } { 7 }$
D)- $- \frac { 9 } { 5 }$

Question 56

Solve the equation.

--4x + 9 - 3x + 10 = 4

A)15
B) $- \frac { 15 } { 7 }$
C) $- \frac { 3 } { 7 }$
D) $\frac { 15 } { 7 }$

Question 57

Write the algebraic expression described.
If x represents the first of four consecutive odd integers, express the sum of the first integer and the fourth integer in terms of x.

A)2x + 8
B)2x + 3
C)2x + 6
D)4x + 12

Question 58

Solve the equation.

- $\frac { \mathrm { n } } { 3 } = 12$

A)14
B)4
C)36
D)15

Question 59

Solve the equation.
3r + 4 = 34

A)27
B)7
C)31
D)10

Question 60

Solve the equation.
6n - 8 = 22

A)24
B)5
C)11
D)28

Question 61

Solve the equation.

- $\frac { \mathrm { f } } { 3 }$ - 5 = 1

A)-18
B)12
C)-12
D)18

Question 62

Solve the equation.

- $\frac { b } { 3 } - 10 = - 6$

A)14
B)12
C)-14
D)-12

Question 63

Solve the equation.

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

A)150
B)75
C)-75
D)-150

Question 64

Solve the equation.

-6p = 5(3p + 5)

A) $\frac { 9 } { 25 }$
B) $- \frac { 25 } { 9 }$
C) $\frac { 25 } { 9 }$
D) $\frac { 25 } { 6 }$

Question 65

Solve the equation.

-12(4c - 4)= 9c - 8

A) $\frac { 40 } { 39 }$
B) $\frac { 40 } { 57 }$
C) $\frac { 56 } { 39 }$
D)- $- \frac { 40 } { 39 }$

Question 66

Solve the equation.

- $\frac { a } { 3 } - \frac { 1 } { 3 } = - 6$

A)-19
B)-17
C)17
D)19

Question 67

Write the algebraic expression described. Simplify if possible.
In the race for Student Body President, Jose received 135 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

A)(x - 135)votes
B)(135 - x)votes
C)(135x)votes
D)(x + 135)votes

Question 68

Solve the equation.

-9p = 7(2p + 3)

A) $- \frac { 21 } { 5 }$
B) $\frac { 21 } { 5 }$
C) $\frac { 5 } { 21 }$
D) $\frac { 7 } { 3 }$

Question 69

Solve the equation.

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

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

Question 70

Solve the equation.
9.4m + 6.9 - 15.4m = -7.1 - 6m + 14

A)0
B)-1.1
C)all real numbers
D)no solution

Question 71

Write the algebraic expression described. Simplify if possible.
A 24-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

A)(z - 24)cm
B)(z + 24)cm
C)(24 - 2z)cm
D)(24 - z)cm

Question 72

Solve the equation.
7(x + 4)= (7x + 28)

A)56
B)0
C)all real numbers
D)no solution

Question 73

Solve the equation.

- $\frac { 3 } { 2 } x + \frac { 1 } { 5 } = \frac { 7 } { 5 } x$

A)-16
B)-2
C)16
D)2

Question 74

Solve the equation.

--8x + 5(3x - 6)= -21 - 2x

A)1
B) $- \frac { 17 } { 3 }$
C)- $- \frac { 51 } { 5 }$
D)- 1

Question 75

Solve the equation.
2(2z - 5)= 3(z + 2)

A)4
B)-4
C)-2
D)16

Question 76

Solve the equation.
5(2z - 4)= 9(z + 3)

A)47
B)7
C)12
D)-7

Question 77

Solve the equation.
2(y + 3)= 3(y - 8)

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

Question 78

Solve the equation.
9x - 8 + 9x - 8 = 9x + 9x - 19

A)0
B)288
C)all real numbers
D)no solution

Question 79

Solve the equation.

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

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

Question 80

Write the algebraic expression described. Simplify if possible.
Two numbers have a sum of 28. If one number is q, express the other number in terms of q.

A)q - 28
B)28 - 2q
C)q + 28
D)28 - q