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Tutorial:
Solving Multi-
Step
Equations
Click here
to begin

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By t he end of t his t ut orial,
you will be able t o:
1. Def ine t he t er ms equation,
coefficient, constant, inver se operation,
and variable
2. Solve a mult i-st ep
equat ion wit h one
variable

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Variable
A variable is a letter used to represent a missing
or unknown number in an equation.
Example A:2 x + 5 = 7
Example B: - 5 n – 20 = 5
var iable
var iable

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Equation
An equation is a statement formed by
placing an equal sign between two
expressions
Example A: 2 x + 5 = 7
Example B: 4 x = 20
Example C:
Non- Example A: 25n
Non- Example B: 2x2
+ 3x + 7
25
3
=
x

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Coefficient
A coefficient is the term that multiplies the
variable in an expression or equation.
Example A: 2 x + 5 = 7
Example B: - 5 n – 20 = 5
coef f icient
coef f icient

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Constant
A constant is the term in an equation that
stands alongside the variable and its
coefficient.
Example A: 2 x + 5 = 7
Example B: - 5 n – 20 = 5
const ant
const ant

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Inverse Operation
An inverse operation is the opposite
operation in an equation that allows
isolation.
Example A: 2 x + 5 = 7
Example B: 5 n = 5
Subt ract ing 5 is t he inverse operat ion
Dividing by 5 is t he inverse operat ion

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Practice: What you’ve learned
Now that we’ve gone over important vocabulary words,
let’s see what you’ve learned. Click the appropriate
letter to answer each question
1. Which of the following is an equation:
2n
2n + 7
2n + 7 = 15
None of these
A
B
D
C

9. 421
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Practice: What you’ve learned
Now that we’ve gone over important vocabulary words,
let’s see what you’ve learned. Click the appropriate letter
to answer each question
1. Which of the following is an equation:
2n
2n + 7
2n + 7 = 15
None of these
A
B
D
C
This is an expression. Click here to go
back and try again.

10. 421
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10
Practice: What you’ve learned
Now that we’ve gone over important vocabulary
words, let’s see what you’ve learned. Click the
appropriate letter to answer each question
1. Which of the following is an equation:
2n
2n + 7
2n + 7 = 15
None of these
A
B
D
C
This is an expression. Click here to go
back and try again

11. 421
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11
Practice: What you’ve learned
Now that we’ve gone over important vocabulary
words, let’s see what you’ve learned. Click the
appropriate letter to answer each question
1. Which of the following is an equation:
2n
2n + 7
2n + 7 = 15
None of these
A
B
D
C
Correct!
Next Quest ion

12. 421
0011 0010 1010 1101 0001 0100 1011
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Practice: What you’ve learned
Now that we’ve gone over important vocabulary
words, let’s see what you’ve learned. Click the
appropriate letter to answer each question
1. Which of the following is an equation:
2n
2n + 7
2n + 7 = 15
None of these
A
B
D
C
Click here to go back and try again

13. 421
0011 0010 1010 1101 0001 0100 1011
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2. A variable is a letter that
represents:
a number
a fraction
an unknown number
None of these
A
B
D
C

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2. A variable is a letter that
represents:
a number
a fraction
an unknown number
None of these
A
B
D
C
Not just a number. Click here to
go back and try again

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2. A variable is a letter that
represents:
a number
a fraction
an unknown number
None of these
A
B
D
C
It can be a fraction, but be more
specific. Click here to go back and try again

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2. A variable is a letter that
represents:
a number
a fraction
an unknown number
None of these
A
B
D
C Correct!
Next Quest ion

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2. A variable is a letter that
represents:
a number
a fraction
an unknown number
None of these
A
B
D
C
Click here to go back and try again

18. 421
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3. What is the inverse operation
of + 7:
divide by 7
subtract 7
multiply by 7
None of these
A
B
D
C

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3. What is the inverse operation
of + 7:
divide by 7
subtract 7
multiply by 7
None of these
A
B
D
C
An inverse operation is the opposite
operation. Click here to go back and try again

20. 421
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3. What is the inverse operation
of + 7:
divide by 7
subtract 7
multiply by 7
None of these
A
B
D
C
Correct
Next Quest ion

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3. What is the inverse operation
of + 7:
divide by 7
subtract 7
multiply by 7
None of these
A
B
D
C
An inverse operation is the opposite
operation. Click here to go back and try again

22. 421
0011 0010 1010 1101 0001 0100 1011
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3. What is the inverse operation
of + 7:
divide by 7
subtract 7
multiply by 7
None of these
A
B
D
C Click here to go back and try again

23. 421
0011 0010 1010 1101 0001 0100 1011
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4. Identify the coefficient in the
equation 3n – 12 = 80:
3
n
12
None of these
A
B
D
C

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4. Identify the coefficient in the
equation 3n – 12 = 80:
3
n
12
None of these
A
B
D
C
Correct
Cont inue
Tut orial

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4. Identify the coefficient in the
equation 3n – 12 = 80:
3
n
12
None of these
A
B
D
C
This is a variable. Click here to go back
and try again.

26. 421
0011 0010 1010 1101 0001 0100 1011
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4. Identify the coefficient in the
equation 3n – 12 = 80:
3
n
12
None of these
A
B
D
C
This is the constant.
Click here to go back and try again

27. 421
0011 0010 1010 1101 0001 0100 1011
27
4. Identify the coefficient in the
equation 3n – 12 = 80:
3
n
12
None of these
A
B
D
C
Click here to go back and try again

28. 421
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How to solve a multi- step
equation with one variable
We will now go t hr ough t he st ep-
by-st ep procedur e in solving a
mult i-st ep equat ion using t he
example 2x + 7 = 15

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2x + 7 = 15
- 7
- 7
First, eliminate the constant by finding its
inverse operation. The equation needs to be
balanced so if you subtract 7 on one side of the
equal sign, you must do the same on the other
side of the equal sign.

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2x + 7 = 15
- 7 - 7
2x = 8
+7 and - 7 cancel out and you are left
with the equation 2x = 8

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2x = 8
2 2
From here you must isolate x by
eliminating the coefficient of 2 through
its inverse operation. Once again, the
equation needs to be balanced. If you
divide by 2 on one side of the equal sign,
you must do the same on the other side
of the equal sign.

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2x = 8
2 2
The 2’s on the left side of the
equation cancel out which
isolates x and leaves or
8 ÷ 2, resulting in x = 4
.
2
8

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Congratulations!
You have just completed this
tutorial. You should now have
the confidence to solve a
multi- step equation.
Click to take the quiz.here

34. 421
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1. What is the term that
stands alongside the variable
and coefficient?
the inverse operation
a fraction
the constant
None of these
A
B
D
C

35. 421
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35
1. What is the term that stands
alongside the variable and
coefficient?
the inverse operation
a fraction
the constant
None of these
A
B
D
C
This is the opposite operation within the
equation. Click here to go
back and try again

36. 421
0011 0010 1010 1101 0001 0100 1011
36
1. What is the term that stands
alongside the variable and coefficient?
the inverse operation
a fraction
the constant
None of these
A
B
D
C
It can be a fraction, but be more specific.
Click here to go back and try again

37. 421
0011 0010 1010 1101 0001 0100 1011
37
1. What is the term that stands
alongside the variable and coefficient?
the inverse operation
a fraction
the constant
None of these
A
B
D
C
Correct!
Click here for the next question

38. 421
0011 0010 1010 1101 0001 0100 1011
38
1. What is the term that stands
alongside the variable and coefficient?
the inverse operation
a fraction
the constant
None of these
A
B
D
C
Click here to go back and try again

39. 421
0011 0010 1010 1101 0001 0100 1011
39
2. What is the term that multiplies
the variable?
the equation
the coefficient
the constant
None of these
A
B
D
C

40. 421
0011 0010 1010 1101 0001 0100 1011
40
2. What is the term that
multiplies the variable?
the equation
the coefficient
the constant
None of these
A
B
D
C
This is an expression set equal
to a solution. Click here to go
back and try again

41. 421
0011 0010 1010 1101 0001 0100 1011
41
2. What is the term that
multiplies the variable?
the equation
the coefficient
the constant
None of these
A
B
D
C
Correct!
Click here for the next question

42. 421
0011 0010 1010 1101 0001 0100 1011
42
2. What is the term that
multiplies the variable?
the equation
the coefficient
the constant
None of these
A
B
D
C
This is the term that stands alongside
the variable and coefficient.
Click here to go back and try again

43. 421
0011 0010 1010 1101 0001 0100 1011
43
2. What is the term that
multiplies the variable?
the equation
the coefficient
the constant
None of these
A
B
D
C
Click here to go back and try again

44. 421
0011 0010 1010 1101 0001 0100 1011
44
3. What is the unknown number
in any equation?
the variable
the constant
the coefficient
None of these
A
B
D
C

45. 421
0011 0010 1010 1101 0001 0100 1011
45
3. What is the unknown number
in any equation?
the variable
the constant
the coefficient
None of these
A
B
D
C
Correct!
Click here for the next question

46. 421
0011 0010 1010 1101 0001 0100 1011
46
3. What is the unknown number
in any equation?
the variable
the constant
the coefficient
None of these
A
B
D
C
This is the term that stands alongside
the variable and coefficient.
Click here to go back and try again

47. 421
0011 0010 1010 1101 0001 0100 1011
47
3. What is the unknown number
in any equation?
the variable
the constant
the coefficient
None of these
A
B
D
C
This is the term that multiplies
the variable. Click here to go back
and try again

48. 421
0011 0010 1010 1101 0001 0100 1011
48
3. What is the unknown number
in any equation?
the variable
the constant
the coefficient
None of these
A
B
D
C
Click here to go back and try again

49. 421
0011 0010 1010 1101 0001 0100 1011
49
4. What is the first step in solving the
equation: 2y + 5 = 1
eliminate the coefficient
2 through division
eliminate 1 through
its inverse operation
eliminate the constant 5
through its inverse operation
guess and check by
plugging in values for x
A
B
D
C

50. 421
0011 0010 1010 1101 0001 0100 1011
50
4. What is the first step in solving the equation: 2y
+ 5 = 1
eliminate the coefficient
2 through division
eliminate 1 through
its inverse operation
eliminate the constant 5
through its inverse operation
guess and check by
plugging in values for x
A
B
D
C
This is the following step.
Click here to go back and try again

51. 421
0011 0010 1010 1101 0001 0100 1011
51
4. What is the first step in solving the equation: 2y
+ 5 = 1
eliminate the coefficient
2 through division
eliminate 1 through
its inverse operation
eliminate the constant 5
through its inverse operation
guess and check by
plugging in values for x
A
B
D
C
Eliminating 1 would make the
equation unbalanced.
Click here to go back and try again

52. 421
0011 0010 1010 1101 0001 0100 1011
52
4. What is the first step in solving the equation: 2y
+ 5 = 1
eliminate the coefficient
2 through division
eliminate 1 through
its inverse operation
eliminate the constant 5
through its inverse operation
guess and check by
plugging in values for x
A
B
D
C Correct!
Click here for the next question.

53. 421
0011 0010 1010 1101 0001 0100 1011
53
4. What is the first step in solving the equation: 2y
+ 5 = 1
eliminate the coefficient
2 through division
eliminate 1 through
its inverse operation
eliminate the constant 5
through its inverse operation
guess and check by
plugging in values for x
A
B
D
C
You can do this, but it may take
a long period of time.
Click here to go back and try again

54. 421
0011 0010 1010 1101 0001 0100 1011
54
5. Solve for the variable: 3g – 1 =
8
3g = 6
g = 3
g = 9/3
None of these
A
B
D
C

55. 421
0011 0010 1010 1101 0001 0100 1011
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5. Solve for the variable: 3g – 1 = 8
3g = 6
g = 3
g = 9/3
None of these
A
B
D
C
The variable g must be isolated
Click here to go back and try again

56. 421
0011 0010 1010 1101 0001 0100 1011
56
5. Solve for the variable: 3g – 1 = 8
3g = 6
g = 3
g = 9/3
None of these
A
B
D
C
Correct!
Click here for the next question.

57. 421
0011 0010 1010 1101 0001 0100 1011
57
5. Solve for the variable: 3g – 1 = 8
3g = 6
g = 3
g = 9/3
None of these
A
B
D
C
You’re almost there.
9/3 must be simplified.
Click here to go back and try again

58. 421
0011 0010 1010 1101 0001 0100 1011
58
5. Solve for the variable: 3g – 1 = 8
3g = 6
g = 3
g = 9/3
None of these
A
B
D
C
Click here to go back and try again

59. 421
0011 0010 1010 1101 0001 0100 1011
59
6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = - 5
x = 5
None of these
A
B
D
C

60. 421
0011 0010 1010 1101 0001 0100 1011
60
6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = - 5
x = 5
None of these
A
B
D
C
You’re almost there.
10/2 must be simplified.
Click here to go back and try again

61. 421
0011 0010 1010 1101 0001 0100 1011
61
6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = - 5
x = 5
None of these
A
B
D
C
Not quite. The solution is opposite in sign.
Click here to go back and try again

62. 421
0011 0010 1010 1101 0001 0100 1011
62
6. Solve for the variable: 2x + 5 =
15
x = 10/2
x = - 5
x = 5
None of these
A
B
D
C Correct!
Click here for the next question

63. 421
0011 0010 1010 1101 0001 0100 1011
63
6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = - 5
x = 5
None of these
A
B
D
C
Click here to go back and try again

64. 421
0011 0010 1010 1101 0001 0100 1011
64
7. Solve for the variable: 3y + 5 = 11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C

65. 421
0011 0010 1010 1101 0001 0100 1011
65
7. Solve for the variable: 3y + 5 = 11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C
Correct!
Click here for the next question

66. 421
0011 0010 1010 1101 0001 0100 1011
66
7. Solve for the variable: 3y + 5 = 11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C
You need to isolate the variable y.
Click here to go back and try again

67. 421
0011 0010 1010 1101 0001 0100 1011
67
7. Solve for the variable: 3y + 5 =
11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C You’re almost there.
6/3 must be simplified.
Click here to go back and try again

68. 421
0011 0010 1010 1101 0001 0100 1011
68
7. Solve for the variable: 3y + 5 =
11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C
Click here to go back and try again

69. 421
0011 0010 1010 1101 0001 0100 1011
69
8. Solve for the variable: 7t – 9 = 19
t = - 28
t = 4
t = 28/7
None of these
A
B
D
C

70. 421
0011 0010 1010 1101 0001 0100 1011
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8. Solve for the variable: 7t – 9 = 19
t = - 28
t = 4
t = 28/7
None of these
A
B
D
C
Check your calculations.
Click here to go back and try again

71. 421
0011 0010 1010 1101 0001 0100 1011
71
8. Solve for the variable: 7t – 9 = 19
t = - 28
t = 4
t = 28/7
None of these
A
B
D
C
Correct!
Click here for results.

72. 421
0011 0010 1010 1101 0001 0100 1011
72
8. Solve for the variable: 7t – 9 = 19
t = - 28
t = 4
t = 28/7
None of these
A
B
D
C
You’re almost there.
28/7 must be simplified.
Click here to go back and try again

73. 421
0011 0010 1010 1101 0001 0100 1011
73
8. Solve for the variable: 7t – 9 = 19
t = - 28
t = 4
t = 28/7
None of these
A
B
D
C
Click here to go back and try again

74. 421
0011 0010 1010 1101 0001 0100 1011
74
Find your percentage by dividing the total
correct by the total number of questions.
8/8 = A+ 6/8 = C
5/8 = D
7/8 = B
4/8 &
Below = F