Deck 2: Equations, Inequalities, and Applications

Question 1

Solve for x. Check your answers.
x + 18 = 19

A)x = 1
B)x = 37
C)x = -37
D)x = -1

Answer 1

A

Question 2

Find the value of x that satisfies the equation.
2.9 = 21.6 - x

A)x = 24
B)x = 18.2
C)x = 24.5
D)x = 18.7

Answer 2

D

Question 3

Find the value of x that satisfies the equation.
8.3 = 15 - x

A)x = 23.3
B)x = 22.8
C)x = 6.2
D)x = 6.7

Answer 3

D

Question 4

Find the value of x that satisfies the equation.
$$x + 1 \frac { 1 } { 2 } = 1 \frac { 2 } { 3 }$$

A) $x = 1$
B) $x = \frac { 3 } { 2 }$
C) $x = \frac { 1 } { 6 }$
D) $x = \frac { 19 } { 6 }$

Question 5

Solve for x. Check your answers.
-9 = x - 7

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

Question 6

Determine if the given solution is correct. If it is not, find the solution.
Is -5 the solution to x + 6 = 5 - 4?

A)no; x = 3
B)no; x = 7
C)yes
D)no; x = 15

Question 7

Find the value of x that satisfies the equation.
$$x - \frac { 1 } { 2 } = \frac { 3 } { 4 }$$

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

Question 8

Find the value of x that satisfies the equation.
$$x - \frac { 13 } { 24 } = - \frac { 3 } { 8 }$$

A) $x = - \frac { 11 } { 12 }$
B) $x = \frac { 11 } { 12 }$
C) $x = \frac { 1 } { 6 }$
D) $x = - \frac { 1 } { 6 }$

Question 9

Solve for x. Check your answers.
17 - 12 = x - 6

A)x = 23
B)x = 35
C)x = 11
D)x = -1

Question 10

Solve for x. Check your answers.
9 + 11 + x = 6 + 8

A)x = 16
B)x = -6
C)x = 34
D)x = -22

Question 11

Determine if the given solution is correct. If it is not, find the solution.
Is -5 the solution to -16 - 8 = x - 17?

A)yes
B)no; x = -41
C)no; x = -25
D)no; x = -7

Question 12

Solve for x. Check your answers.
5 - 17 + 8 = 6 + x - 3

A)x = 33
B)x = -7
C)x = -13
D)x = 5

Question 13

Find the value of x that satisfies the equation.
-0.6 + x = 17

A)x = 17.6
B)x = 17.1
C)x = 16.4
D)x = 15.9

Question 14

Solve for x. Check your answers.
-10 = x - 3

A)x = 13
B)x = 7
C)x = -7
D)x = -13

Question 15

Find the value of x that satisfies the equation.
$$\frac { 1 } { 2 } + x = 5$$

A) $x = \frac { 9 } { 2 }$
B) $x = 2$
C) $\mathrm { x } = 9$
D) $x = \frac { 11 } { 2 }$

Question 16

Solve for x. Check your answers.
-16 = x - 14

A)x = 2
B)x = -30
C)x = 224
D)x = -2

Question 17

Find the value of x that satisfies the equation.
-7.5 + x = 17.2

A)x = 9.2
B)x = 24.7
C)x = 24.2
D)x = 9.7

Question 18

Find the value of x that satisfies the equation.
$$x + \frac { 4 } { 7 } = \frac { 6 } { 7 }$$

A) $x = 2$
B) $x = \frac { 10 } { 7 }$
C) $x = \frac { 5 } { 7 }$
D) $x = \frac { 2 } { 7 }$

Question 19

Find the value of x that satisfies the equation.
$$\frac { 3 } { 8 } - \frac { 1 } { 2 } = x - \frac { 3 } { 16 }$$

A) $x = - \frac { 5 } { 16 }$
B) $x = \frac { 7 } { 32 }$
C) $x = \frac { 17 } { 16 }$
D) $x = \frac { 1 } { 16 }$

Question 20

Solve for x. Check your answers.
x - 5 = 18

A)x = -23
B)x = 23
C)x = -13
D)x = 13

Question 21

Determine if the given solution is correct. If it is not, find the solution.
Is 13 the solution to -4 + x = 10?

A)no; x = 14
B)no; x = -14
C)yes
D)no; x = 6

Question 22

Solve for x. Be sure to reduce your answer. Check your solution.
$$- \frac { 1 } { 3 } x = - 5$$

A) $x = - 8$
B) $x =$
C) $x = - 9$
D) $x =$

Question 23

Solve for x. Be sure to reduce your answer. Check your solution.
-30.4 = -7.6x

A)x = 2
B)x = 4
C)x = 22.8
D)x = -22.8

Question 24

Find the value of the variable that satisfies the equation.
$$3 \mathrm { x } + 16 \mathrm { x } = 15$$

A) $x = 285$
B) $x = - 4$
C) $x = \frac { 19 } { 15 }$
D) $x = \frac { 15 } { 19 }$

Question 25

Find the value of the variable that satisfies the equation.
2x - 3 = 9

A)x = 7
B)x = 6
C)x = 10
D)x = 14

Question 26

Solve for x. Be sure to reduce your answer. Check your solution.
$$\frac { 3 } { 10 } x = \frac { 3 } { 10 }$$

A) $x =$
B) $x = 12$
C) $x = 13$
D) $x =$

Question 27

Find the value of the variable that satisfies the equation.
$$\frac { 1 } { 5 } x - \frac { 1 } { 5 } = - 6$$

A) $x = - 29$
B) $x = 29$
C) $x = 31$
D) $x = - 31$

Question 28

Solve for x. Be sure to reduce your answer. Check your solution.
$$\frac { x } { 4 } = 5$$

A) $x = 9$
B) $x = 1$
C) $x = 20$
D) $x = 8$

Question 29

Determine if the given solution is correct. If it is not, find the solution.
Is -11 the solution to -x = 11

A)no; x = 11
B)yes
C)no; x = -1
D)no; x = 0

Question 30

Solve for x. Be sure to reduce your answer. Check your solution.
-8x = -32

A)x = 2
B)x = 24
C)x = 4
D)x = -24

Question 31

Find the value of the variable that satisfies the equation.
$$- 2 x - 12 x = - 17$$

A) $x = 238$
B) $x = \frac { 17 } { 14 }$
C) $x = - 3$
D) $x = \frac { 14 } { 17 }$

Question 32

Find the value of the variable that satisfies the equation.
$$5 x + 10 = 1 - 2 x$$

A) $x = \frac { 7 } { 9 }$
B) $x = - \frac { 9 } { 7 }$
C) $x =ـــ$
D) $x = - \frac { 7 } { 9 }$

Question 33

Find the value of the variable that satisfies the equation.
-10x + x = -36

A)x = -4
B)x = 4
C)x = 5
D)x = -5

Question 34

Find the value of the variable that satisfies the equation.
$$50 + 14 x = 4 x$$

A) $x = - 5$
B) $x =$
C) $\mathrm { x } =$
D) $x = - 6$

Question 35

Determine if the given solution is correct. If it is not, find the solution.
Is $\frac { 58 } { 5 }$ the solution to $5 x = 53$

A) yes
B) no; $x = 265$
C) no; $x = \frac { 53 } { 5 }$
D) no; $x = \frac { 5 } { 53 }$

Question 36

Find the value of the variable that satisfies the equation.
$$\frac { 1 } { 2 } x - 5 = 1$$

A) $x = 8$
B) $x = - 8$
C) $x = - 12$
D) $x = 12$

Question 37

Solve for x. Be sure to reduce your answer. Check your solution.
$$\frac { 1 } { 8 } x = 0$$

A) $x =$
B) $x = - 8$
C) $x = 1$
D) $x = 0$

Question 38

Find the value of the variable that satisfies the equation.
$$- 8 x + 1 + 6 x = - 3 x + 6$$

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

Question 39

Find the value of the variable that satisfies the equation.
4x + x = 45 A) $x = 9$
B) $x = 8$
C) $x = \frac { 45 } { 4 }$
D) $x = \frac { 23 } { 2 }$

Question 40

Find the value of the variable that satisfies the equation.
$$8 x + 2 = 66$$

A) $x = 56$
B) $x = 60$
C) $x = 6$
D) $x = 8$

Question 41

Solve for x. Be sure to reduce your answer. Check your solution.
4x = -28

A)x = 32
B)x = -7
C)x = 1
D)x = -32

Question 42

Find the value of the variable that satisfies the equation.
$$\frac { x } { 7 } + 6 = 14$$

A) $x = 15$
B) $x = 142$
C) $x = 56$
D) $x = 140$

Question 43

Find the value of the variable that satisfies the equation.
$$- 4 x - 10 = - 1 - 8 x$$

A) $x = - \frac { 4 } { 9 }$
B) $x =ـــ$
C) $x = -$
D) $x = -$

Question 44

Determine whether the given solution is correct. If it is not, find the solution.
Is 9 the solution for -9x + 4 + 7x = -3x + 9?

A)Yes
B)No; x = -4
C)No; x = 5
D)No; x = -9

Question 45

Determine whether the given solution is correct. If it is not, find the solution.
$\frac { 1 } { 2 } x - \left( x - \frac { 1 } { 9 } \right) = \frac { 1 } { 18 } ( x + 1 )$

A) $x = - \frac { 3 } { 10 }$
B) $x = \frac { 1 } { 8 }$
C) $x = - \frac { 1 } { 26 }$
D) $x = \frac { 1 } { 10 }$

Question 46

Find the value of the variable that satisfies the equation.
$$- 4 x = - 11 x + 42$$

A) $x = \frac { 1 } { 6 }$
B) $x = - \frac { 21 } { 2 }$
C) $x = - \frac { 14 } { 5 }$
D) $x = 6$

Question 47

Determine whether the given solution is correct. If it is not, find the solution.
Is 42 a solution to $x - 5 = \frac { 6 } { 7 } x + 1$ ?

A) $\mathrm { Yes }$
B) No

Question 48

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { - 6 x + 5 } { 4 } + 1 = - \frac { 7 x } { 3 }$$

A) $x = - \frac { 3 } { 10 }$
B) $x = \frac { 3 } { 10 }$
C) $x = \frac { 27 } { 46 }$
D) $x = - \frac { 27 } { 10 }$

Question 49

Determine whether the given solution is correct. If it is not, find the solution.
Is $- \frac { 12 } { 17 }$ the solution for $7 x + 5 = - 7 - 10 x ?$

A) Yes
B) No; $x = -$
C) No; $x = - \frac { 17 } { 12 }$
D) $\mathrm { No } ; \mathrm { x } = \frac { 17 } { 12 }$

Question 50

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 1 } { 5 } ( x + 6 ) = \frac { 1 } { 6 } ( x + 8 )$$

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

Question 51

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 2 } { 5 } x - \frac { 1 } { 3 } x = 4$$

A) $x = - 60$
B) $x = - 120$
C) $x = 60$
D) $x = 120$

Question 52

Determine whether the given solution is correct. If it is not, find the solution.
-0.08y + 0.14(3000 - y)= 0.28y

A)y = 840
B)y = 210
C)y = 2100
D)y = 2520

Question 53

Determine whether the given solution is correct. If it is not, find the solution.
-0.15(40)+ 0.6x = 0.3(40 + x)

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

Question 54

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 1 } { 4 } x - \frac { 3 } { 8 } x = 5$$

A) $x = 35$
B) $x = 40$
C) $x = - 35$
D) $x = - 40$

Question 55

Determine whether the given solution is correct. If it is not, find the solution.
$$x - \frac { 1 } { 2 } x - 3 = 1$$

A) $x = 8$
B) $x = - 4$
C) $x = 4$
D) $x = - 8$

Question 56

Determine whether the given solution is correct. If it is not, find the solution.
Is 5 the solution for -9x + 6 + 7x = -3x + 11?

A)No; x = 11
B)No; x = -6
C)Yes
D)No; x = -11

Question 57

Determine whether the given solution is correct. If it is not, find the solution.
Is $\frac { 9 } { 17 }$ the solution for $- 5 x + 7 = - 10 + 4 x ?$

A) $\mathrm { No } ; \mathrm { x } = \frac { 17 } { 9 }$
B) No; $x = \frac { 1 } { 3 }$
C) No; $x = - \frac { 9 } { 17 }$
D) Yes

Question 58

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 1 } { 6 } ( x - 12 ) - \frac { 1 } { 2 } ( x - 2 ) = x - 8$$

A) $x = \frac { 33 } { 4 }$
B) $x = \frac { 15 } { 4 }$
$\mathrm { C } ) \mathrm { x } = \frac { 27 } { 4 }$
D) $x = \frac { 21 } { 4 }$

Question 59

Determine whether the given solution is correct. If it is not, find the solution.
0.8x - 0.4(20 + x)= 0.40(20)

A)x = 30
B)x = 20
C)x = 50
D)x = 40

Question 60

Determine whether the given solution is correct. If it is not, find the solution.
$\frac { 1 } { 3 } x - \frac { 1 } { 3 } = - 5$

A) $x = - 16$
B) $x = 16$
C) $x = 14$
D) $x = - 14$

Question 61

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 4 ( 7 - x ) } { 3 } = x$$

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

Question 62

Determine whether the given solution is correct. If it is not, find the solution.
$$\frac { 3 ( y - 2 ) } { 5 } = 1 - 3 y$$

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

Question 63

Determine whether the given solution is correct. If it is not, find the solution.
1.5x + 4.3 = 0.7x + 2.54

A)x = -2.21
B)x = -2.2
C)x = -2.222
D)x = -0.455

Question 64

Determine whether the given solution is correct. If it is not, find the solution.
Is 4 a solution to $\frac { 1 } { 4 } ( x + 6 ) = \frac { 1 } { 8 } x + 1 ?$
B) No

Question 65

Write an algebraic expression for the quantity. Let x represent the unknown value.
Ten greater than a number.

A)x + 10
B)x > 10
C)x - 10
D)10 > x

Question 66

Solve.
$$7 ( x + 4 ) + 4 = 7 x + 2$$

A) Infinite number of solutions
B) No solution
C) $x = 30$
D) $x = 10$

Question 67

Solve.
$$18 x + 11 ( x + 1 ) = 29 ( x + 1 ) - 18$$

A) Infinite number of solutions
B) No solution
C) $x = 1$
D) $x = 0$

Question 68

Write an algebraic expression for the quantity. Let x represent the unknown value.
A value decreased by six. A) $x - 6$
B) $6 - x$
C) $\frac { 6 } { x }$
D) $x + 6$

Question 69

Solve.
$$8 ( x + 1 ) = 33 x + 33 - 25 x - 25$$

A) $x = 1$
B) Infinite number of solutions
C) $x = 0$
D) No solution

Question 70

Write an algebraic expression for the quantity. Let x represent the unknown value.
Ten divided by a number. A) $\frac { 10 } { x }$
B) $10 - \mathrm { x }$
C) $\frac { x } { 10 }$
D) $10 \mathrm { x }$

Question 71

Solve.
$$7 x - 3 - 2 x + 1 = 9 x - 4 x - 5$$

A) Infinite number of solutions
B) $x = - 64$
C) $x = 0$
D) No solution

Question 72

Solve.
$$6 ( x + 5 ) = 6 x + 30$$

A) $x = 0$
B) Infinite number of solutions
C) $x = 60$
D) No solution

Question 73

Determine whether the given solution is correct. If it is not, find the solution.
Is $- 4$ a solution to $\frac { 1 } { 3 } ( x + 6 ) = \frac { 1 } { 6 } x + \frac { 4 } { 3 } ?$

A) Yes
B) $\mathrm { No }$

Question 74

Write an algebraic expression for the quantity. Let x represent the unknown value.
Two times the sum of a number and four.

A)4x + 2
B)2(x + 4)
C)2x + 4
D)4(x + 2)

Question 75

Solve.
$$- 4 ( x + 7 ) + 86 = 2 x - 6 ( x - 5 )$$

A) $x =$
B) $x =$
C) Infinite number of solutions
D) No solution

Question 76

Write an algebraic expression for the quantity. Let x represent the unknown value.
Four less than a number.

A)x - 4
B)x < 4
C)4 < x
D)4 - x

Question 77

Write an algebraic expression for the quantity. Let x represent the unknown value.
Eight less than double a number.

A)8 - 2x
B)2x - 8
C)8x - 2
D)2 - 8x

Question 78

Write an algebraic expression for the quantity. Let x represent the unknown value.
Three-fourths of a quantity. A) $\frac { 3 } { 4 } - x$
B) $x - \frac { 3 } { 4 }$
C) $\frac { 3 x } { 4 }$
D) $\frac { 3 } { 4 } + x$

Question 79

Write an algebraic expression for the quantity. Let x represent the unknown value.
A quantity increased by 25.

A)x - 25
B)x + 25
C)25x $$\text { D) } \frac { 25 } { x }$$

Question 80

Solve.
$$- 7 x + 9 + 5 x = - 2 x + 14$$

A) $x = 5$
B) No solution
C) Infinite number of solutions
D) $x = - 9$