Deck 2: Solving Equations and Inequalities

Question 1

Solve the equation using the addition principle.
$$t + 3 \frac { 1 } { 2 } = 5 \frac { 1 } { 2 }$$

A) 2
B) 9
C) 5
D) 4

Answer 1

A

Question 2

Decide if the given number is a solution to the given equation.

- $$\frac { x } { 9 } = 8 ; 72$$

Answer 2

True

Question 3

Decide if the given number is a solution to the given equation.

- $$2 x = 16 ; 6$$

Answer 3

False

Question 4

Solve the equation using the addition principle.
$$z - 22.43 = 0$$

A) $- 21.43$
B) $22.43$
C) $- 22.43$
D) $21.43$

Question 5

Solve the equation using the addition principle.
$$- 20 = b - 2$$

A) 18
B) $- 22$
C) 22
D) $- 18$

Question 6

Decide if the given number is a solution to the given equation.

- $$\mathrm { p } - 7 = 1 ; 8$$

Question 7

Solve the equation using the addition principle.
$$- 7 + b = 11$$

A) $- 18$
B) 4
C) $- 4$
D) 18

Question 8

Solve the equation using the addition principle.
$$a - 8 = - 7$$

A) $- 15$
B) $- 1$
C) 15
D) 1

Question 9

Solve the equation using the addition principle.
$$a + 1 = 3$$

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

Question 10

Solve the equation using the addition principle.
$$8 = z + 7$$

A) 15
B) $- 15$
C) 1
D) $- 1$

Question 11

Decide if the given number is a solution to the given equation.

- $$\mathrm { p } + 5 = 16 ; 11$$

Question 12

Solve the equation using the addition principle.
$$h - \frac { 1 } { 3 } = \frac { 7 } { 9 }$$

A) 4
B) $\frac { 4 } { 9 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 10 } { 9 }$

Question 13

Solve the equation using the addition principle.
$$x - \frac { 15 } { 23 } = - \frac { 3 } { 23 }$$

A) $- \frac { 12 } { 23 }$
B) $- \frac { 18 } { 23 }$
C) $\frac { 18 } { 23 }$
D) $\frac { 12 } { 23 }$

Question 14

Solve the equation using the addition principle.
$$- 24.7 = 29.8 + x$$

A) $- 5.1$
B) $5.1$
C) $54.5$
D) $- 54.5$

Question 15

Solve the equation using the addition principle.
$$h + \frac { 1 } { 2 } = \frac { 3 } { 4 }$$

A) 3
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 5 } { 4 }$

Question 16

Solve using the multiplication principle.
$$7 x = 28$$

A) 21
B) 4
C) $\frac { 1 } { 4 }$
D) 196

Question 17

Decide if the given number is a solution to the given equation.

- $$6 m + 4 = 18 ; 2$$

Question 18

Solve the equation using the addition principle.
27 = -21 + z A) 48
В) $- 6$
C) 6
D) $- 48$

Question 19

Decide if the given number is a solution to the given equation.

- $$9 p + 3 p - 4 = 32 ; \quad 3$$

Question 20

Solve the equation using the addition principle.
$$\frac { 1 } { 3 } + x = 4$$

A) 11
B) $\frac { 11 } { 3 }$
C) 1
D) $\frac { 13 } { 3 }$

Question 21

Solve using the multiplication principle.
$$- \frac { 1 } { 7 } y = 16$$

A) $- 105$
В) $- 96$
C) $- 23$
D) $- 112$

Question 22

Solve using the multiplication principle.
$$- 7 \mathrm {~b} = 119$$

A) $- 126$
B) 126
C) $- 17$
D) 1

Question 23

Solve using the multiplication principle.
$$\frac { 4 } { 7 } y = - \frac { 4 } { 5 }$$

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

Question 24

Solve using the multiplication principle.
$$- \frac { 1 } { 2 } \mathrm { k } = - 10$$

A) 20
B) 4
C) $- 2$
D) 5

Question 25

Solve using the multiplication principle.
$$\frac { m } { - 5 } = 17$$

A) $- 68$
B) $- 22$
C) $- 80$
D) $- 85$

Question 26

Solve using the multiplication principle.
$$- \frac { 1 } { 5 } \mathrm { z } = \frac { 1 } { 8 }$$

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

Question 27

Solve using the multiplication principle.
$$49 = - 7 \mathrm { k }$$

A) $- 7$
B) 1
C) 56
D) $- 56$

Question 28

Solve using the multiplication principle.
$$\frac { - t } { 8 } = 21$$

A) $- 168$
B) $- 147$
C) $- 29$
D) $- 160$

Question 29

Solve using the multiplication principle.
$$- 4 s = - 68$$

A) $- 64$
B) 2
C) 17
D) 64

Question 30

Solve using the multiplication principle.
$$15 = 5 x$$

A) 10
B) $\frac { 1 } { 3 }$
C) 75
D) 3

Question 31

Solve using the multiplication principle.
$$\frac { 9 } { 10 } x = 27$$

A) $\frac { 243 } { 10 }$
B) $\frac { 279 } { 10 }$
C) $\frac { 261 } { 10 }$
D) 30

Question 32

Solve using the multiplication principle.
$$- 112 = - 7 n$$

A) 16
B) 2
C) 105
D) $- 105$

Question 33

Solve using the multiplication principle.
$$\frac { 5 } { 6 } = \frac { 1 } { 2 } x$$

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

Question 34

Solve using the multiplication principle.
$$- 126 = 9 z$$

A) 1
B) $- 135$
C) $- 14$
D) 135

Question 35

Solve using the multiplication principle.
$$\frac { 8 } { 21 } x = - \frac { 8 } { 5 }$$

A) $- \frac { 7 } { 15 }$
B) $- \frac { 12 } { 35 }$
C) $- \frac { 35 } { 12 }$
D) $- \frac { 21 } { 5 }$

Question 36

Solve using the multiplication principle.
$$\frac { x } { 3 } = 14$$

A) 17
B) 39
C) 28
D) 42

Question 37

Solve using the multiplication principle.
$$\frac { 1 } { 4 } \mathrm { x } = 15$$

A) 56
B) 45
C) 19
D) 60

Question 38

Solve using the multiplication principle.
$$- 2 x = - 18$$

A) 9
B) 16
C) $- 16$
D) 2

Question 39

Solve using the multiplication principle.
$$- 7 a = 35$$

A) $- 5$
B) $- 42$
C) 42
D) 1

Question 40

Solve using the multiplication principle.
$$- x = - 11$$

A) $- 10$
B) $- \frac { 1 } { 11 }$
C) $- 11$
D) 11

Question 41

Solve using the multiplication principle.
$$- \frac { 7 } { 3 } x = - 32.27$$

A) $13.83$
B) $29.27$
C) $16.39$
D) $6.83$

Question 42

Solve using the multiplication principle.
$$53.4 = 8.9 y$$

A) $47.4$
B) 6
C) $\frac { 1 } { 6 }$
D) $44.5$

Question 43

Solve using the multiplication principle.
$$- 9.9 y = 39.6$$

A) $- 29.7$
B) $- 4$
$C ) - \frac { 1 } { 4 }$
D) $- 35.6$

Question 44

Solve.
$$9 x + 5 = - 22$$

A) $- \frac { 17 } { 9 }$
B) $- 3$
C) $- 36$
D) $- 2$

Question 45

Solve using the multiplication principle.
$3.1 \mathrm { t } = - 27.9$

A) $- \frac { 1 } { 9 }$
B) $- 9$
C) $- 24.8$
D) $- 18.9$

Question 46

Solve using the multiplication principle.
$$8.3 x = 58.1$$

A) $\frac { 1 } { 7 }$
B) 7
C) $49.8$
D) $51.1$

Question 47

Solve using the multiplication principle.
$$\frac { 1 } { 9 } \mathrm {~b} = - 3.00$$

A) $- 27.00$
B) $- 3.00$
C) $6.00$
D) $5.00$

Question 48

Solve using the multiplication principle.
$$- \frac { 3 } { 4 } x = 9.12$$

A) $- 12.16$
B) $- 8.96$
C) $- 9.16$
D) $- 5.12$

Question 49

Solve using the multiplication principle.
$$- 4.8 m = - 14.4$$

A) $11.4$
B) 3
C) $\frac { 1 } { 3 }$
D) $9.6$

Question 50

Solve using the multiplication principle.
$$39.2 \mathrm { x } = 274.4$$

A) $267.4$
B) $\frac { 1 } { 7 }$
C) $235.2$
D) 7

Question 51

Solve using the multiplication principle.
$$18.3 \mathrm { t } = - 91.5$$

A) $- 5$
В) $- 73.2$
C) $- 86.5$
D) $- \frac { 1 } { 5 }$

Question 52

Solve using the multiplication principle.
$$- \frac { 4 } { 21 } y = - \frac { 24 } { 35 }$$

A) $\frac { 18 } { 5 }$
B) $\frac { 45 } { 8 }$
C) $\frac { 9 } { 10 }$
D) $\frac { 8 } { 45 }$

Question 53

Solve.
$$7 n - 10 = 11$$

A) 18
B) 11
C) 3
D) 14

Question 54

Solve.
$$7 r + 8 = 64$$

A) 8
B) 49
C) 1
D) 53

Question 55

Solve using the multiplication principle.
$$- 37.6 = 9.4 z$$

A) $- 28.2$
B) $- 33.6$
C) $- \frac { 1 } { 4 }$
D) $- 4$

Question 56

Solve using the multiplication principle.
$$- 48.3 y = 821.1$$

A) $- 17$
B) -804.1
C) $- \frac { 1 } { 17 }$
D) $- 772.8$

Question 57

Solve.
$$178 = 12 x + 10$$

A) 4
B) 14
C) 156
D) 160

Question 58

Solve.
$$10 = 6 x - 2$$

A) 6
B) 2
C) 10
D) 3

Question 59

Solve.
$$4 + 10 p = - 6$$

A) 1
B) $- \frac { 1 } { 5 }$
C) $- \frac { 3 } { 10 }$
$D ) - 1$

Question 60

Solve using the multiplication principle.
$- 19.2 \mathrm {~m} = - 153.6$

A) $\frac { 1 } { 8 }$
B) 8
C) $145.6$
D) $134.4$

Question 61

Solve.
$$\frac { 1 } { 4 } a - \frac { 1 } { 4 } = - 6$$

A) $- 23$
B) 23
C) 25
D) $- 25$

Question 62

Solve. Clear fractions first.
$$x + \frac { 1 } { 2 } x = 27$$

A) 18
B) 9
C) 54
D) 21

Question 63

Solve.
$$9 x - 3 + 3 x = 6 x + 77 - 4 x$$

A) 8
B) 10
C) 7
D) 9

Question 64

Solve. Clear fractions first.
$$\frac { 1 } { 3 } r + 2 = \frac { 1 } { 6 } r + \frac { 4 } { 3 }$$

A) 4
B) 3
C) $- 4$
D) $- 12$

Question 65

Solve. Clear fractions first.
$$\frac { 2 } { 5 } x - \frac { 1 } { 3 } x = 3$$

A) $- 45$
B) 45
C) 90
D) $- 90$

Question 66

Solve.
$$- 8 b + 1 + 6 b = - 3 b + 6$$

A) 5
B) $- 6$
C) $- 1$
D) 6

Question 67

Solve.
$$- 40 = - 8 x + 8$$

A) 44
B) $- 6$
C) 40
D) 6

Question 68

Solve.
$$12 - 10 x = 3 x - 2 x - 65$$

A) $\frac { 65 } { 9 }$
B) $\frac { 53 } { 9 }$
C) $\frac { 65 } { 11 }$
D) 7

Question 69

Solve.
$$- 2 \mathrm { x } - 18 = - 58$$

A) 20
В) $- 20$
C) $- 38$
D) 38

Question 70

Solve.
$- 6 a + 3 + 7 a = 5 - 28$

A) $- 36$
B) 36
C) 26
D) $- 26$

Question 71

Solve.
$$9 x + 2 x = 22$$

A) 2
B) $\frac { 11 } { 9 }$
C) $\frac { 22 } { 0 }$
D) 11

Question 72

Solve.
$$5 x - 1 = 77 - 8 x$$

A) $- 6$
B) $- 26$
C) $- \frac { 76 } { 3 }$
D) 6

Question 73

Solve.
$$- 9 n - 3 = 78$$

A) $- 72$
B) $- 9$
C) 9
D) 76

Question 74

Solve.
$$6 x + 5 = 3 x + 26$$

A) $\frac { 31 } { 9 }$
B) 7
C) 9
D) $\frac { 7 } { 3 }$

Question 75

Solve. Clear fractions first.
$$\frac { 1 } { 3 } y - 9 = 4$$

A) 41
В) $- 39$
C) $- 41$
D) 39

Question 76

Solve. Clear fractions first.
$$\frac { 5 } { 3 } y - 25 = - 15$$

A) $- 6$
B) 2
C) 24
D) 6

Question 77

Solve.
$$\frac { 1 } { 5 } \mathrm { f } - 5 = 1$$

A) 20
В) 30
C) $- 20$
D) $- 30$

Question 78

Solve.
$$7 y - 5 = 49 + y$$

A) $\frac { 22 } { 3 }$
B) $\frac { 11 } { 2 }$
C) $\frac { 27 } { 4 }$
D) 9

Question 79

Solve.
$$- 3 x - 7 x = - 60$$

A) $- 6$
B) 7
C) 6
D) $- 50$

Question 80

Solve.
$$8 y - 15 = 3 y$$

A) $\frac { 15 } { 11 }$
B) $- 3$
C) 3
D) $- \frac { 15 } { 11 }$