Deck 3: Equations, Inequalities and Problem Solving

Question 1

If a satisfies an equation, then it is a root of the equation.

Answer 1

True

Question 2

Use the properties of equality to solve the equation. u $-$ 0.11 = $-$ 0.77

A) u = -0.61
B) u = -0.66
C) u = -0.56
D) u = -0.71
E) none of these

Answer 2

u = -0.66

Question 3

Use the properties of equality to solve the equation. $\frac { t } { 10 } = 11$

A) t = 21
B) t = 110
C) t = 11
D) t = 10
E) none of these

Answer 3

t = 110

Question 4

Use the properties of equality to solve the equation. $-$ 17 = u + 15

A) u = -32
B) u = -22
C) u = -37
D) u = -27
E) none of these

Question 5

Use the properties of equality to solve the equation. $\frac { 3 } { 22 } u = \frac { 1 } { 11 }$

A) $u = \frac { 1 } { 22 }$
B) $u = \frac { 2 } { 11 }$
C) $u = \frac { 1 } { 3 }$
D) $u = \frac { 2 } { 3 }$
E) none of these

Question 6

Use the properties of equality to solve the equation. 2 u = $-$ 20

A) u = -5
B) u = -15
C) u = $-$ 10
D) u = 0
E) none of these

Question 7

Use the properties of equality to solve the equation. u + 0.37 = 0.77

A) u = 0.45
B) u = 0.5
C) u = 0.35
D) u = 0.4
E) none of these

Question 8

Use the properties of equality to solve the equation. $\frac { - p } { 5 } = \frac { 1 } { 16 }$

A) $p = - \frac { 5 } { 16 }$
B) $p = - \frac { 1 } { 16 }$
C) $p = \frac { 16 } { 5 }$
D) $p = - \frac { 16 } { 5 }$
E) none of these

Question 9

Use the properties of equality to solve the equation. m + 4 = 20

A) m = 26
B) m = 21
C) m = 16
D) m = 11
E) none of these

Question 10

The addition-subtraction property of equality state that any number, except 0, can be added to or subtracted from both sides of an equation to produce equivalent equations.

Question 11

Use the properties of equality to solve the equation. $-$ 1 = u + 9

A) u = -5
B) u = -10
C) u = -15
D) u = 0
E) none of these

Question 12

Use the properties of equality to solve the equation. 10 = t $-$ 1

A) t = 9
B) t = 11
C) t = 6
D) t = 21
E) none of these

Question 13

Use the properties of equality to solve the equation. $-$ 1 = $-$ 17 u

A) $u = \frac { 1 } { 17 }$
B) $u = - \frac { 1 } { 17 }$
C) $u = \frac { 4 } { 21 }$
D) $u = - \frac { 3 } { 19 }$
E) none of these

Question 14

The multiplication-division property of equality states that an equivalent equation is obtained whenever both sides of a given equation are mulitplied or divided by the same real number.

Question 15

Solving an equation refers to the process of determining the solution set.

Question 16

Use the properties of equality to solve the equation. $\frac { 7 } { 16 } t = - \frac { 3 } { 28 }$

A) $t = - \frac { 4 } { 7 }$
B) $t = - \frac { 1 } { 49 }$
C) $t = - \frac { 12 } { 49 }$
D) $t = - \frac { 4 } { 49 }$
E) none of these

Question 17

Use the properties of equality to solve the equation. $x - \frac { 2 } { 7 } = \frac { 2 } { 3 }$

A) $x = 1 \frac { 1 } { 20 }$
B) $x = \frac { 20 } { 21 }$
C) $x = \frac { 2 } { 7 }$
D) $x = \frac { 1 } { 21 }$
E) none of these

Question 18

Use the properties of equality to solve the equation. $\frac { 7 t } { 8 } = \frac { 7 } { 64 }$

A) $t = 64$
B) $t = \frac { 7 } { 8 }$
C) $t = \frac { 1 } { 8 }$
D) $t = 8$
E) none of these

Question 19

Use the properties of equality to solve the equation. x $-$ 6 = 1

A) x = 2
B) x = 17
C) x = 7
D) x = -5
E) none of these

Question 20

Use the properties of equality to solve the equation. $\frac { 5 } { 8 } u = 40$

A) u = 64
B) u = 59
C) u = 65
D) u = 69
E) none of these

Question 21

Use the properties of equality to solve the equation. 3.1 x = 11.16

A) x = 3.7
B) x = 3.6
C) x = 3.55
D) x = 3.65
E) none of these

Question 22

Use the properties of equality to solve the equation. Enter your answer in fraction form.

Question 23

Use the properties of equality to solve the equation. 7.92 = 2.4 t Please express your answer as a decimal.

Question 24

Use the properties of equality to solve the equation. 2.3 m = 4.83

A) m = 2.2
B) m = 2.1
C) m = 2.15
D) m = 2.05
E) none of these

Question 25

Use the properties of equality to solve the equation. 5 t = 30

Question 26

Use the properties of equality to solve the equation. m 0.29 = 0.86

Question 27

Use the properties of equality to solve the equation. 5 = m + 8

Question 28

Use the properties of equality to solve the equation. 32 = 5 u Enter your answer in fraction form.

Question 29

Use the properties of equality to solve the equation. 1.7 a = 6.97 Please express your answer as a decimal.

Question 30

Use the properties of equality to solve the equation. 13 = m 15

Question 31

Use the properties of equality to solve the equation.

Question 32

Use the properties of equality to solve the equation. $- \frac { 7 } { 8 } t = 1$

A) $t = - \frac { 1 } { 8 }$
B) $t = - \frac { 7 } { 8 }$
C) $t = - \frac { 1 } { 7 }$
D) $t = - \frac { 8 } { 7 }$
E) none of these

Question 33

Use the properties of equality to solve the equation. $- \frac { 3 } { 16 } a = 1$

A) $a = - \frac { 1 } { 16 }$
B) $a = - \frac { 16 } { 3 }$
C) $a = - \frac { 1 } { 3 }$
D) $a = - \frac { 3 } { 16 }$
E) none of these

Question 34

Use the properties of equality to solve the equation. x 11 = 18

Question 35

Use the properties of equality to solve the equation. $- 2 m = \frac { 1 } { 9 }$

A) $m = - \frac { 9 } { 2 }$
B) $m = - \frac { 1 } { 18 }$
C) $m = - \frac { 2 } { 9 }$
D) $m = - \frac { 1 } { 2 }$
E) none of these

Question 36

Use the properties of equality to solve the equation.

Question 37

Use the properties of equality to solve the equation. $\frac { - a } { 5 } = \frac { 1 } { 2 }$

A) $a = - \frac { 1 } { 2 }$
B) $a = - \frac { 2 } { 5 }$
C) $a = - \frac { 5 } { 2 }$
D) $a = \frac { 2 } { 5 }$
E) none of these

Question 38

Use the properties of equality to solve the equation. m + 8 = 3

Question 39

Use the properties of equality to solve the equation. 7.56 = 2.1 t

A) t = 3.7
B) t = 3.65
C) t = 3.55
D) t = 3.6
E) none of these

Question 40

Use the properties of equality to solve the equation. t + 0.92 = 0.14

Question 41

Use the properties of equality to solve the equations and match with a correct solution.

- $t = - \frac { 1 } { 50 }$

A) $- 5 t = \frac { 1 } { 10 }$
B) $- 3 t = \frac { 1 } { 7 }$

Question 42

Use the properties of equality to solve the equation.

Question 43

Use the properties of equality to solve the equation.

Question 44

Use the properties of equality to solve the equation. 1.6 m = 3.36 Please express your answer as a decimal.

Question 45

Use the properties of equality to solve the equation. p 0.44 = 0.63

Question 46

Use the properties of equality to solve the equation. Enter your answer in fraction form.

Question 47

Use the properties of equality to solve the equation. Enter your answer in fraction form.

Question 48

Use the properties of equality to solve the equation.

Question 49

Use the properties of equality to solve the equation. 9 t = 90

Question 50

Use the properties of equality to solve the equation. 5.94 = 2.2 m Please express your answer as a decimal.

Question 51

Use the properties of equality to solve the equation. x 11 = 17

Question 52

Use the properties of equality to solve the equation.

Question 53

Use the properties of equality to solve the equation.

Question 54

Use the properties of equality to solve the equation. x + 0.19 = 0.26

Question 55

Use the properties of equality to solve the equation.

Question 56

Use the properties of equality to solve the equation. 12 = a 12

Question 57

Use the properties of equality to solve the equation.

Question 58

Use the properties of equality to solve the equation. Enter your answer in fraction form.

Question 59

Use the properties of equality to solve the equation.

Question 60

Use the properties of equality to solve the equation. 1 = t + 20

Question 61

Solve the equation. 24 $-$ 16 a = 24

A) a = 12
B) a = 1.5
C) a = 9.5
D) a = 3

Question 62

Solve the equation. $-$ 6 t + 4 = 34

A) t = $-$ 5
B) t = 5
C) t = $-$ 7
D) t = 7
E) t = $-$ 10

Question 63

Solve the equation. 3 c + 5 = 20

A) c = 13
B) c = 5
C) c = 12
D) c = 1

Question 64

Solve the equation. 54 = $-$ 4 $-$ 13 a

A) $a = \frac { 58 } { 13 }$
B) $a = - \frac { 58 } { 13 }$
C) $a = \frac { 50 } { 13 }$
D) $a = - \frac { 13 } { 58 }$
E) $a = - \frac { 50 } { 13 }$

Question 65

The quotient of a number and five is 30 is translated as $\frac { 5 } { n } = 30$ .

Question 66

Solve the equation. $-$ 4 c + 4 = 12

A) c = 5
B) c = 1
C) c = 2
D) c = -2

Question 67

Solve the equation. 8 = 6 b $-$ 4

A) b = 1
B) b = 2
C) b = 9
D) b = 8

Question 68

Use the properties of equality to solve the equations and match with a correct solution.

- $t = - \frac { 1 } { 21 }$

A) $- 5 t = \frac { 1 } { 10 }$
B) $- 3 t = \frac { 1 } { 7 }$

Question 69

Solve the equation. 27 $-$ 18 a = 45

A) a = 4
B) a = 7.5
C) a = 2
D) a = 14
E) a = $-$ 4

Question 70

Solve the equation. $-$ 5 t + 2 = 32

A) t = $-$ 6
B) t = 6
C) t = $-$ 12
D) t = $-$ 7
E) t = 7

Question 71

Solve the equation. 24 = $-$ 3 $-$ 13 b

A) $b = - \frac { 27 } { 13 }$
B) $b = - \frac { 21 } { 13 }$
C) $b = \frac { 27 } { 13 }$
D) $b = \frac { 21 } { 13 }$

Question 72

The multiplication-division property is always used before the addition-subtraction property.

Question 73

Solve the equation. 23 $-$ z = 27

A) z = -1
B) z = -3
C) z = -4
D) z = 2

Question 74

Sometimes more than one equation is used to solve a word problem.

Question 75

Solve the equation. 18 = $-$ 2 $-$ 5 a

A) a = $-$ 2
B) a = 4
C) a = $-$ 6
D) a = $-$ 4
E) a = 6

Question 76

Two less than four times a number is 30 is translated as $4 n - 2 = 30$ .

Question 77

Solve the equation. 5 b $-$ 4 = 26

A) b = 11
B) b = 2
C) b = 10
D) b = 6
E) none of these

Question 78

Solve the equation. $-$ 2 y + 6 = 16

A) y = -4
B) y = -5
C) y = 1
D) y = 5
E) none of these

Question 79

Solve the equation. 17 = $-$ 4 $-$ 7 a

A) a = 3
B) a = $-$ 2
C) a = 4
D) a = $-$ 3
E) a = $-$ 4

Question 80

Solve the equation. 6 t $-$ 4 = 8

A) t = 6
B) t = 8
C) t = 1
D) t = 2