equation tutorial with practice quiz
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Tutorial:Solving Multi-
StepEquations
Click here to begin
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By the end of this tutorial, you will be able to:
1. Define the terms equation, coefficient, constant, inverse operation, and variable
2. Solve a multi-step equation with 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
variable
variable
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EquationAn 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: 25nNon-Example B: 2x2 + 3x + 7
253
x
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CoefficientA 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
coefficient
coefficient
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ConstantA 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
constant
constant
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Inverse OperationAn inverse operation is the opposite operation in an equation that allows isolation.
Example A: 2 x + 5 = 7
Example B: 5 n = 5
Subtracting 5 is the inverse operation
Dividing by 5 is the inverse operation
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Practice: What you’ve learnedNow 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:
2n2n + 72n + 7 = 15None of these
A
B
D
C
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Practice: What you’ve learnedNow 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 + 72n + 7 = 15None of these
A
B
D
C
This is an expression. Click here to goback and try again.
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Practice: What you’ve learnedNow 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:
2n2n + 72n + 7 = 15None of these
A
B
D
C
This is an expression. Click here to go back and try again
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Practice: What you’ve learnedNow 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:
2n2n + 72n + 7 = 15None of these
A
B
D
CCorrect!
Next Question
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Practice: What you’ve learnedNow 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:
2n2n + 72n + 7 = 15None of these
A
B
D
C
Click here to go back and try again
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2. A variable is a letter that represents:
a numbera fractionan unknown numberNone of these
A
B
D
C
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2. A variable is a letter that represents:
a numbera fractionan unknown numberNone 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 numbera fractionan unknown numberNone of these
A
B
D
C
It can be a fraction, but be morespecific. Click here to go back and try again
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2. A variable is a letter that represents:
a numbera fractionan unknown numberNone of these
A
B
D
C Correct!
Next Question
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2. A variable is a letter that represents:
a numbera fractionan unknown numberNone of these
A
B
D
C
Click here to go back and try again
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3. What is the inverse operation of + 7:
divide by 7subtract 7multiply by 7None of these
A
B
D
C
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3. What is the inverse operation of + 7:
divide by 7subtract 7multiply by 7None of these
A
B
D
C
An inverse operation is the oppositeoperation. Click here to go back and try again
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3. What is the inverse operation of + 7:
divide by 7subtract 7multiply by 7None of these
A
B
D
C
Correct
Next Question
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3. What is the inverse operation of + 7:
divide by 7subtract 7multiply by 7None of these
A
B
D
C
An inverse operation is the oppositeoperation. Click here to go back and try again
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3. What is the inverse operation of + 7:
divide by 7subtract 7multiply by 7None of these
A
B
D
C Click here to go back and try again
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4. Identify the coefficient in the equation 3n – 12 = 80:
3n12None of these
A
B
D
C
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4. Identify the coefficient in the equation 3n – 12 = 80:
3n12None of these
A
B
D
C
Correct
ContinueTutorial
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4. Identify the coefficient in the equation 3n – 12 = 80:
3n12None of these
A
B
D
C
This is a variable. Click here to go backand try again.
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4. Identify the coefficient in the equation 3n – 12 = 80:
3n12None of these
A
B
D
CThis is the constant.
Click here to go back and try again
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4. Identify the coefficient in the equation 3n – 12 = 80:
3n12None of these
A
B
D
C
Click here to go back and try again
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How to solve a multi-step equation with one variable
We will now go through the step-by-step procedure in solving a multi-step equation using the example 2x + 7 = 15
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2x + 7 = 15 - 7 -7First, 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 2From 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
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1. What is the term that stands alongside the variable and coefficient?
the inverse operationa fractionthe constantNone of these
A
B
D
C
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1. What is the term that stands alongside the variable and coefficient?
the inverse operationa 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
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1. What is the term that stands alongside the variable and coefficient?
the inverse operation
a fractionthe constantNone 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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1. What is the term that stands alongside the variable and coefficient?
the inverse operationa fractionthe constantNone of these
A
B
D
CCorrect!
Click here for the next question
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1. What is the term that stands alongside the variable and coefficient?
the inverse operation
a fraction
the constantNone of these
A
B
D
C
Click here to go back and try again
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2. What is the term that multiplies the variable?
the equationthe coefficientthe constantNone of these
A
B
D
C
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2. What is the term that multiplies the variable?
the equationthe coefficientthe constantNone of these
A
B
D
C
This is an expression set equal to a solution. Click here to go
back and try again
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2. What is the term that multiplies the variable?
the equationthe coefficientthe constantNone of these
A
B
D
C
Correct!Click here for the next question
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2. What is the term that multiplies the variable?
the equationthe coefficientthe constantNone of these
A
B
D
CThis is the term that stands alongside
the variable and coefficient.Click here to go back and try again
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2. What is the term that multiplies the variable?
the equationthe coefficientthe constantNone of these
A
B
D
C
Click here to go back and try again
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3. What is the unknown number in any equation?
the variablethe constantthe coefficientNone of these
A
B
D
C
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3. What is the unknown number in any equation?
the variablethe constantthe coefficientNone of these
A
B
D
C
Correct!Click here for the next question
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3. What is the unknown number in any equation?
the variablethe constantthe coefficientNone of these
A
B
D
C
This is the term that stands alongsidethe variable and coefficient.
Click here to go back and try again
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3. What is the unknown number in any equation?
the variablethe constantthe coefficientNone of these
A
B
D
CThis is the term that multiplies
the variable. Click here to go back and try again
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3. What is the unknown number in any equation?
the variablethe constantthe coefficientNone of these
A
B
D
C
Click here to go back and try again
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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
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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
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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
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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
CCorrect!
Click here for the next question.
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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
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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
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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 isolatedClick here to go back and try again
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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
Correct!Click here for the next question.
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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
CYou’re almost there.
9/3 must be simplified.Click here to go back and try again
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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
Click here to go back and try again
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6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = -5
x = 5
None of these
A
B
D
C
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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
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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
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6. Solve for the variable: 2x + 5 = 15
x = 10/2
x = -5
x = 5
None of these
A
B
D
CCorrect!
Click here for the next question
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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
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7. Solve for the variable: 3y + 5 = 11
y = 2
3y = 6
y = 6/3
None of these
A
B
D
C
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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
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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
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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
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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
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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
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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
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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
Correct!Click here for results.
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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
CYou’re almost there.
28/7 must be simplified.Click here to go back and try again
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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
Click here to go back and try again
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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
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