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Unit 4: ONE STEP EQUATIONS

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MGSE6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

MGSE.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

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ONE STEP EQUATIONS

What you do to the LEFT side of the
equation must also be done to the
RIGHT side to keep it balanced.

An equation is like a balance scale
because it shows that two
quantities are equal.

Fill in the Blanks

ONE STEP EQUATIONS

• What is the variable?

To solve one step equations, you need

to ask three questions about the

equation:

• What operation is performed on the variable?
• What is the inverse operation?

(The one that will undo what is being
done to the variable)

ONE STEP EQUATIONS

Example 1 Solve x + 4 = 12

What is the variable?

Using the subtraction property of equality, subtract 4 from both
sides of the equation.

- 4

x

x + 4 = 12

What is the inverse operation (the one that will undo what is
being done to the variable)?

What operation is being performed on the variable?

- 4

8=

The subtraction property of equality tells us to subtract
the same thing on both sides to keep the equation equal.

Subtraction.

Addition.

The variable is x.

ONE STEP EQUATIONS

Example 2 Solve y - 7 = 13

What is the variable?

Using the addition property of equality, add 7 to both sides of
the equation.

y - 7 = 13
+ 7

y

The variable is y.

Subtraction.

Addition.

What operation is being performed on the variable?
What is the inverse operation (the one that will undo what is being
done to the variable)?

+ 7

= 20

The addition property of equality tells us to add the same
thing on both sides to keep the equation equal.

Multiple Choice

y - 7 = 13

• 6

• 91

• 20

Multiple Choice

The operation that undoes another operation is called

• Substitution

• Variable

• Inverse Operation

• Coefficient

Draw

Solve 6a = 12

ONE STEP EQUATIONS

Example 3 Solve 6a = 12

What is the variable?

Using the division property of equality, divide both sides of the
equation by 6.

6a = 12
6

a

What operation is being performed on the variable? Multiplication.
What is the inverse operation (the one that will undo what is being done
to the variable)?
Division

6

= 2

The division property of equality tells us to divide the same
thing on both sides to keep the equation equal.

The variable is a.

Multiple Choice

$$\frac{b}{2}\ =\ 12$$  

• 14

• 10

• 6

• 24

ONE STEP EQUATIONS

Example 4 Solve

What is the variable?

Using the multiplication property of equality, multiply both sides
of the equation by 2.

= 10

b

The variable is b.

What operation is being performed on the variable? Division.
What is the inverse operation (the one that will undo what is
being done to the variable)?

Multiplication

= 10

2 •

• 2

= 20

= 10

The multiplication property of equality tells us to multiply
the same thing on both sides to keep the equation equal.

Multiple Choice

6t = 60

• t = 66

• t = 10

• t = 54

• t = 0

Multiple Choice

$$\frac{f}{20}\ =\ 100$$  

• 2000

• 4

• 120

• 80

Multiple Choice

56 = 8k

• 64

• 12

• 7

• 48

One-Step Equations

Addition, Subtraction, & Division

What is a one-step equation?

An equation where you only need to do one operation to solve for x.

What is an operation?

• addition

• subtraction

• multiplication

• division

To solve a one-step equations, you need to use the INVERSE operation.

Inverse means opposite

One-Step Equations

To solve a one-step equations, you need to use the inverse (opposite) operation.

using inverse operations (opposite)

​

isolate the variable

Multiple Choice

How do you solve?

$$x+5=10$$  

• $$-5\ on\ both\ sides$$  

• $$+5\ on\ both\ sides$$  

• $$\div5\ on\ both\ sides$$  

• $$\times5\ on\ both\ sides$$  

Multiple Choice

How do you solve?

$$x-3=4$$  

• $$-3\ on\ both\ sides$$  

• $$+3\ on\ both\ sides$$  

• $$\times3\ on\ both\ sides$$  

• $$\div3\ on\ both\ sides$$  

Multiple Choice

How do you solve?

$$3x\equiv12$$  

• $$+3\ on\ both\ sides$$  

• $$-3\ on\ both\ sides$$  

• $$\div3\ on\ both\ sides$$  

Solve for X

Multiple Choice

Solve:

$$x+5=10$$  

• $$x=5$$  

• $$x=15$$  

• $$x=50$$  

Multiple Choice

Solve:

$$x-3=12$$  

• $$x=9$$  

• $$x=15$$  

• $$x=4$$  

Multiple Choice

Solve:

$$3x=12$$  

• $$x=9$$  

• $$x=15$$  

• $$x=4$$  

Multiple Choice

y - 33 = 147

• y = 114

• y = 177

• y = 180

• Answer not Given

Multiple Choice

Solve the equation:
20.5 = x + 4

• 16.5

• 16.05

• 24.5

• 24.05

Multiple Choice

Which equation has w = 8 as the solution?

• 8w= 64

• 16w = 240

• 16 - w = 9

• 4 + w = 10

Multiple Choice

Twice a number is 24.

• 2n = 24

• 2/n = 24

• 2 + n = 24

• 2 - n = 24

Multiple Choice

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3

Multiple Choice

Solve the equation
3x = 27. 

• x = 24

• x = 81

• x = 9

Multiple Choice

Which equation has x = 5 as the solution?

• x + 15 = 10

• 2x = 5

• 2x = 10

Multiple Choice

What is the solution for x + 9 = 21

• 10
• 12
• 11
• 13

Multiple Choice

x - 8 = -5 

• 13
• -13
• 3
• -3

Multiple Choice

m+13=21

• m=34
• m=8
• m=273
• m=6

Multiple Choice

Solve for y:
y - 7 = 10

• 17
• -3
• 3
• -17

Multiple Choice

Solve the equation:
4p = 16

• p = 12
• p = 64
• p = 3
• p = 4

Multiple Choice

Solve the equation:
2w=58

• w = 29
• w = 32
• w = 15
• w = 116

Multiple Choice

Solve the equation:
x/3 = 4

• x = 12
• x = 1
• x = 16
• x = 3

Multiple Choice

Solve for x:

• 20
• 7
• 10
• 3

Multiple Choice

What is the inverse (opposite) of addition?

Multiple Choice

What is the inverse (opposite) of subtraction?

Multiple Choice

What is the inverse (opposite) of multiplication?

Multiple Choice

What is the inverse (opposite) of division?

Multiple Choice

How do you solve?

$$x+5=10$$  

• $$-5\ on\ both\ sides$$  

• $$+5\ on\ both\ sides$$  

• $$\div5\ on\ both\ sides$$  

• $$\times5\ on\ both\ sides$$  

Multiple Choice

How do you solve?

$$x-3=4$$  

• $$-3\ on\ both\ sides$$  

• $$+3\ on\ both\ sides$$  

• $$\times3\ on\ both\ sides$$  

• $$\div3\ on\ both\ sides$$  

Multiple Choice

How do you solve?

$$3x\equiv12$$  

• $$+3\ on\ both\ sides$$  

• $$-3\ on\ both\ sides$$  

• $$\div3\ on\ both\ sides$$  

Multiple Choice

Solve the equation: 
x + 7 = 12

• x = 5
• x = 19
• x = 4
• x = 84

Multiple Choice

Solve the equation:
4p = 16

• p = 12
• p = 64
• p = 3
• p = 4

Multiple Choice

What is the solution of the equation? 
8 = x + 1

• 9
• 7
• 6
• 8

Multiple Choice

y - 33 = 147

• y = 114
• y = 177
• y = 180
• Answer not Given

Multiple Choice

$$k+19=10$$   

• k = 190

• k = -9

• k = 29

• k = 10/19

Multiple Choice

$$\frac{n}{2\ }=\ -6$$  

• n = -12

• n = -4

• n = -3

• n = -8

Multiple Choice

$$7a\ =\ 21$$  

• a = 3

• a = 14

• a = 28

• a = 2

Multiple Choice

$$\frac{b}{5}\ =4$$  

• b = 9

• b = 1

• b = 20

• b = 15

Multiple Choice

What is the solution for x + 9 = 21

• 10
• 12
• 11
• 13

Multiple Choice

x - 8 = -5 

• 13
• -13
• 3
• -3

Multiple Choice

m+13=21

• m=34
• m=8
• m=273
• m=6

Multiple Choice

Solve for y:
y - 7 = 10

• 17
• -3
• 3
• -17

Multiple Choice

k+8=15

• k=23
• k=10
• k=7
• k=11

Multiple Choice

7 + g = 11

• g = 4

• g = -4

• g = 18

• g = -18

Multiple Choice

Solve for z in the following equation:

z - 33 = 147

• z= 114

• z = 177

• z = 180

• No Solution

Multiple Choice

y - 4.6 = 12

• 16.6
• 5.8
• 7.4
• Answer not Given

Multiple Choice

x + 12 = 20

• x = 32
• x = -32
• x = 8
• x = -8

Multiple Choice

Solve for x:

x + 19.46 = 245.3

• 264.76

• 12.6

• 50.7

• 225.84

Multiple Choice

$$k+19=10$$   

• k = 190

• k = -9

• k = 29

• k = 10/19

Multiple Choice

$$21\ =\ 14\ +\ x$$  

• x = 7

• x = 35

• x = 294

• x = 1.5

Multiple Choice

$$\frac{w}{15}=-9$$  

• w = -3/5

• w = 6

• w = -24

• w = -135

Multiple Choice

$$-14\ =\ j\ -\ 20$$  

• j = -7/10

• j = -34

• j = 280

• j = 6

Multiple Choice

$$110\ =\ -11m$$  

• m = 99

• m = -10

• m = 121

• m = -1210

Multiple Choice

$$-18r\ =\ 54$$  

• r = 36

• r = -3

• r = 1/3

• r = -972

Multiple Choice

$$-10\ =\ g\ -\ 2$$  

• g = -5

• g = -8

• g = -12

• g = -20

Multiple Choice

$$\frac{n}{15}=\ -10$$  

• n = -2/3

• n = 5

• n = -150

• n = -25

Multiple Choice

$$a\ -\ 19\ =\ -30$$  

• a = -570

• a = -49

• a = 2

• a = -11

Multiple Choice

$$y\ -\ 7\ =\ -5$$  

• y = -35

• y = 2

• y = -12

• y = 5/7

Multiple Choice

$$-11p\ =\ -44$$  

• p = -55

• p = -33

• p = 484

• p = 4

Multiple Choice

$$\frac{n}{2\ }=\ -6$$  

• n = -12

• n = -4

• n = -3

• n = -8

Multiple Choice

$$-24\ =\ d\ -\ 8$$  

• d = -192

• d = -32

• d = 3

• d = -16

Multiple Choice

$$15y\ =90$$  

• y = 75

• y = 1350

• y = 105

• y = 6

Multiple Choice

$$\frac{a}{3}=\ 15$$  

• a = 45

• a = 18

• a = 12

• a = 5

Multiple Choice

Solve the equation

x + 3 = 5

• 2

• -2

• 8

• -8

Multiple Choice

m - 4 = 10

• -6

• 6

• -14

• 14

Multiple Choice

3r=12

• 36

• 9

• 15

• 4

Multiple Choice

$$\frac{z}{2}=6$$  

• 3

• 4

• 8

• 12

Multiple Choice

f + 5 = -6

• -11

• 1

• -1

• -30

Multiple Choice

j - 3 = 4

• 1

• -1

• 7

• -7

Multiple Choice

-5 x = - 10

• 2

• 50

• 15

• -50

Multiple Choice

$$\frac{x}{10}=1$$  

• 9

• $$\frac{1}{10}$$  

• 10

• 11

Multiple Choice

k + $$\frac{1}{2}$$  = $$\frac{1}{2}$$  

• 1

• 0

• $$\frac{1}{2}$$  

• $$\frac{1}{4}$$  

Multiple Choice

• 14

• -14

• -5

• 5

Multiple Choice

What is the inverse operation that should be performed to solve this equation?

2y = 12

• addition

• subtraction

• multiplication

• division

Multiple Choice

When solving an equation

What ever you do to one side you must _____________.

• do by following the rules

• do to the other side

• do it quickly

Multiple Choice

x - (-2) = 8

• 6

• -6

• 10

• -10

Multiple Choice

An equation always has a

• =

• +

• -

• *

Multiple Choice

What is the value of x in this equation?

• 5

• 15

• 50

• -5

Multiple Choice

$$\frac{w}{2}=20$$  

• 10

• 18

• 40

Multiple Choice

$$\frac{z}{2}=6$$  

• 3

• 4

• 8

• 12

Multiple Choice

Solve: c - 8 = -12

• -20

• 20

• -4

• 4

Multiple Choice

Solve: -11x = 55

• x = -5

• x = 5

• x = 44

• x = -44

Multiple Choice

x - 8 = -5 

• 13
• -13
• 3
• -3

Multiple Choice

• -10
• 50
• -70
• 10

Multiple Choice

Solve:

x - 2.3 = 3.07

• x = 5.37

• x = 0.77

• x = 7.061

• x = 1.33

Multiple Choice

Solve:  $$b\div7\ =\ 1.8$$  

• b = 12.6

• b = 1.26

• b = .27

• No correct answer