7.

6.

EOC Practice

sets?

9.

HLA#3 Review:

Name:Period:Date:Topic: Solving One-Step EquationsEssential Question: How can you solve equations?

Vocabulary:Isolate = using properties of equality and inverse operations to get variable with a coefficient of one alone on one side of the equation. Example: x – 4 = 5 x = 9

Inverse operation = operations that undo one another. Example: Addition and Subtraction Multiplication and Division

Equations: Addition & Subtraction

To solve an equation, you will move terms from one side of the equal sign to the other by using inverse operations.

•GOAL: to isolate the variable.

x + 5 = 7

Think of the situation like this:

There is a house with two rooms

One room has an “x” in it, the other does not

x + 5

The wall between the rooms is where the “=“ sign is.

=

“x” wants to be completely alone in his room. So any other object in that room

has to be moved to the other room, BY YOU!

7

Example:

We need to get the “x” ALONE!

Identify which objectwhich object is in the “x” room

Object to move: the “5”x + 5 = 7

Which operationWhich operation ( +, -, x, ) is attaching the “5” to the “x”?

We must use the Opposite Operation

Operation being used: “+”

Opposite of “+”:

“-”

So we must subtract 5 to get the “x” alone in his room.

x + 5 = 7

Now that we know what to do, How do we do it?

We know we must subtract the “5” to get rid of it.But in equations, whatever you do to one side,

you must also do to the other side. This keeps the equation “balanced”.

So we will subtract 5 from each side of the equal sign.

x + 5 = 7Subtract 5 from each side

On the left, 5 - 5 = 0On the right, 7 - 5 = 2

x + 5 - 5 = 7 - 5

x = 2

Once the “x” is alone on one side,the other side is the answer.

ANSWER:

We need to get the “x” ALONE!

Identify which objectwhich object is in the “x” room

Object to move: the “8”x + 8 = 20

Which operationWhich operation ( +, -, x, ) is attaching the “8” to the “x”?

We must use the Opposite Operation

Operation being used: “+”

Opposite of “+”:

“-”

So we must subtract 8 to get the “x” alone in his room.

x + 8 = 20Subtract 8 from each side

On the left, 8 - 8 = 0On the right, 20 - 8 = 12

x + 8 - 8 = 20 - 8

x = 12Once the “x” is alone on one side,

the other side is the answer.

ANSWER:

15 = x - 9

We need to get the “x” ALONE!

Identify which objectwhich object is in the “x” room

Object to move: the “9”15 = x - 9

Which operationWhich operation ( +, -, x, ) is attaching the “9” to the “x”?

We must use the Opposite Operation

Operation being used: “-”

Opposite of “-”:

“+”

So we must add 9 to get the “x” alone in his room.

Note: x can be on either side of the equal sign!

15 = x - 9Add 9 to each side

On the left, 15 + 9 = 24n the right, -9 + 9 = 0

15 + 9 = x - 9 + 9

24 = xOnce the “x” is alone on one side,

the other side is the answer.

ANSWER:

Pair – Practice:

Page 85 (10, 14, 20 25)Page 87 (80, 84)

Equations: Multiplication & Division

To solve an equation, you will move terms from one side of the equal sign to the other by using inverse operations.

•GOAL: to isolate the variable.

Remember:

2x = 16

We need to get the “x” ALONE!

Identify which objectwhich object is in the “x” room

Object to move: the “2”2x = 16

Which operationWhich operation ( +, -, x, ) is attaching the “2” to the “x”?

We must use the Opposite Operation

Operation being used: “x”

Opposite of “x”:

“”

So we must divide by 2 to get the “x” alone in his room.

Note: when a number sits next to a variable with nothing in between the two, the operation is

multiplication.(two times “x”) is written as “2x”.

2x = 16

Divide each side by two

On the left, 2 ÷ 2 = 1 On the right, 16 ÷ 2 = 8

x = 8Once the “x” is alone on one side,

the other side is the answer.

ANSWER:

2x = 16 2 2

If a number sits next to a variable

with nothing in between the two, the operation is multiplication.

We show division by using fraction

bars.

-3x = 21Divide each side by negative 3

On the left, (-3) ÷ (-3) = 1 On the right, 21 ÷ (-3)= -7

x = -7Once the “x” is alone on one side,

the other side is the answer.

ANSWER:

-3x = 21-3 -3

Note: Which operation is between the (-3) and the x.

If a number sits next to a variable

with nothing in between the two, the operation is multiplication.

-32 = 4x

Divide each side by 4

On the left, -32 ÷ 4 = -8 On the right, 4 ÷ 4 = 1

-8 = xOnce the “x” is alone on one side,

the other side is the answer.

ANSWER:

-32 = 4x4 4

Note: The “x” can be on either side of the equal sign

If a number sits next to a variable

with nothing in between the two, the operation is multiplication.

x = 35

We need to get the “x” ALONE!

Identify which objectwhich object is in the “x” room

Object to move: the “2”x = 8

Which operationWhich operation ( +, -, x, ) is attaching the “2” to the “x”?

We must use the Opposite Operation

Operation being used:

“”

Opposite of “”: “x”

So we must multiply by 2 to get the “x” alone in his room.

Note: When a number is written as a fraction, the operation is division.

(“x” divided by 2) is written as “x/2”.

2

Multiply each side by 2

On the left, 2 ÷ 2 = 1 On the right, 8 x 2 = 16

x = 16Once the “x” is alone on one side,

the other side is the answer.

ANSWER:

x = 82

x = 82

(2)(2)

2 x = 34

Page 85 (26, 30, 36, 40, 42)

Pair-Practice:

Independent Practice!!!

Page 85 - 87 (1-3, 12, 26, 37, 71,80)

•Summary•HLA#4: Hand-Out

Wrap-up: