Solving One-Step Linear Equations

Open Ended

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Review

Multiple Choice

What is Inverse Operation?

• Same Operation

• Opposite operation

• Happy Operation

Multiple Choice

What is the Inverse Operation of +

• $$-$$

• X

• $$\div$$

Multiple Choice

What is the Inverse Operation of $$-$$

• $$-$$

• $$+$$

• $$\div$$

• $$\times$$

Math Response

Solve for x.

x + 7 = 10

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

Solve for x.

x - 5 = 12

Type answer here

Correct Answer: 17

Deg^°

Rad

Math Response

Solve for x.

-2 = x + (-10)

Type answer here

Correct Answer: 8

Deg^°

Rad

Math Response

Solve for x.

n - 13 = -20

Type answer here

Correct Answer: -7

Deg^°

Rad

Multiplication and Division One Step Equations

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Integers

• In order to solve one step equations, you need to be able to complete operations with integers (adding, subtracting, multiplying and dividing).

• Integers are positive and negative whole numbers.

  
  

Important Vocabulary for Equations

• Variable – is a symbol, commonly a single letter, that represents a number.  

• Coefficient - A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. 

• Constant - is a number on its own

Solving Equations

• When solving equations, think of the equation as a scale. Each side of the equals sign must remain “balanced.”

• Whatever you do to one side, you MUST do it to the other.

• The goal of solving equations is to get one variable by itself on one side of the equals sign.

• You will use inverse operations to "undo" the problem to solve for the variable.

6x = 36

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-2x = 82

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Multiple Choice

-20 = 4x

• 5

• -5

• 4

• 3

Multiple Choice

-8y = 24

• 5

• -2

• -3

• 4

Fill in the Blanks

-9d = -72

Multiple Choice

$$\frac{y}{-3\ }=\ -8$$  

• 20

• 24

• 32

• 16

Multiple Choice

$$-7\ =\ \frac{m}{5}$$  

• -30

• -35

• -40

• 30

Fill in the Blanks

$\frac{m}{2}=\ -10$  

Lelah sent 574 text messages last week. On average, how many messages did she send each day?

• Let m represent the number of messages lelah sent.

• Write an equation

• 574 = 7m ( The reason we use is 7 is because there are 7 days in a week)

• Now solve (divide both sides by 7)

• M= 82

Fill in the Blanks

The distance d that lee travels on his bike at a rate of 20 miles per hour for 4 hours is given by the equation

$\frac{d}{4}=\ 20\$  . How far did he ride?

Multiple Choice

What is the inverse operation you would use to solve:

6x = 36

• Multiply

• Divide

• Add

• Subtract

Multiple Choice

Solve the equation:

4p = 16

• p = 12

• p = -12

• p = -4

• p = 4

Multiple Choice

Solve the equation:

-5x = 25

• x = 20

• x = -20

• x = -5

• x = 5

Multiple Choice

9n = -9

• 0

• -1

• -81

• -18

Multiple Choice

-10z = 40

• z = 50

• z = 30

• z = -4

• z = 4

Multiple Choice

3x = -15

• -18

• -5

• x = 5

• x=12

Multiple Choice

What is the inverse operation of multiplication?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

What is the inverse operation of division?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

The main goal of solving equations is to get the _________ by itself.

• Coefficient
• Variable
• Constant
• Term

Multiple Choice

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3

Multiple Choice

Solve for the missing variable:

• m = 5
• m = 1/5
• m = 25
• m = 55

Multiple Choice

Which equation has x = 5 as the solution?

• x + 15 = 10

• 2x = 5

• 2x = 10

Multiple Choice

x + 12 = 20

• x = 32

• x = -32

• x = 8

• x = -8

Multiple Choice

-16+ x= -15

• 2
• 0
• -1
• 1

Multiple Choice

The variable, k, is being divided by 11. How should you show your work to isolate the variable?

• Divide both sides by 11

• Multiply both sides by 11.

• Add 11 to both sides.

• Subtract 11 to both sides.

Multiple Choice

What equation matches this situation? Robyn had some video games then bought 4 more.  Now she has a total of 10 games.

• v - 4 = 10

• v + 4 = 10

• 10 - 4 = v

• Answer not Given

Multiple Choice

5 less than a number is 15.

• x - 5 = 15

• 5 - x = 15

• 15 - x = 5

Multiple Choice

Twice a number is 24.

• 2n = 24

• 2/n = 24

• 2 + n = 24

• 2 - n = 24

Multiple Choice

What does "difference" mean?

• add

• subtract 

• multiply

• divide

Multiple Choice

What is the difference between an expression and equation?

• Expressions do not have an equal sign and equations do have an equal sign

• There is not a difference

Multiple Choice

Why do you divide by 5?

• To undo multiplication, you must divide.

• To undo multiplication, you must multiply by 5 on both sides.

Multiple Choice

The variable, k, is being divided by 11. How should you isolate the variable?  $$16=\frac{k}{11}$$  

• Divide both sides by 11

• Multiply both sides by 11.

• Add 11 to both sides.

• Subtract 11 to both sides.

Multiple Choice

What is the inverse operation of division?

• Division

• Multiplication

• Addition

• Subtraction

Multiple Choice

From this equation, name the variable. $$3x=7$$  

• 7

• 3

• x

• -4

Multiple Choice

$$\frac{x}{5}=3$$  

• x=15

• x=2

• x=8

• x=53

Multiple Choice

10x = 90

• x = 80

• x = 100

• x = 10

• x = 9

Multiple Choice

x ÷ 2 = 12

• x = 24
• x = 6
• x = 20
• x = 10

Multiple Choice

5m = 10  solve for m

• 50
• 15
• 5
• 2

Multiple Choice

Solve for x:

• x = 20
• x = 7
• x = 10
• x = 3

Multiple Choice

3c = 12

• 36

• 4

• 15

• 9

Multiple Choice

Solve the equation:
-5x = 25

• x = 20
• x = -20
• x = -5
• x = 5

Multiple Choice

Solve the equation
3x = 27. 

• x = 24
• x = 81
• x = 9

Multiple Choice

y/3=12

• 36
• -36
• 4
• -4

Multiple Choice

Translate 4 more than x equals 7 into an equation and solve. 

• x+4=7
  x = 11
• x+4=7
  x = 3
• x-4=7
  x = 11
• x-4=7
  x=3

Multiple Choice

Which of the following is used to solve single step equations mathematically?

• substitution
• inverse operations
• frequency
• data analysis

Multiple Choice

When solving an equation, our goal is to:

• add all the numbers together.
• use a calculator.
• eat lunch.
• isolate the variable to solve.

Multiple Choice

Using the "opposite operation" to "undo" and isolate the variable when solving an equation is more commonly called...

• Inverse operations
• math
• variable
• PEMDAS

Multiple Choice

Which choice models this situation?

Anna participated in a read-a-thon. Mr. Cole pledged $4 per book and gave Anna $44. How many books did Anna read?

• b - 4 = 44

• b + 4 = 33

• 4b = 44

• b/4 = 44