s olving o ne and t wo s tep e quations algebra 1 mr. bise
TRANSCRIPT
SOLVING ONE AND TWO STEP EQUATIONSAlgebra 1
Mr. Bise
SOLVING ONE-STEP EQUATIONS To Solve an Equation, you will move terms from
one side of the equal sign to the other.
GOAL: Get the “x” (the variable) alone on one side of the equal sign.
STRANGER DANGER!
TOOL: Inverse Operations
The Three Simplest Inverse Operations: Addition and Subtraction (Positive and Negative) Multiplication and Division (Multiply by the
Reciprocal) Roots and Exponents
Addition & Subtraction (Positive and Negative)
Equations
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 anyone else in that room is the Stanger Danger
and has to be moved to the other room, BY YOU!
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THINK OF THE SITUATION LIKE THIS:
Identify who is in the “x” room that shouldn’t be there.
The Stranger Danger: the “5”x + 5 = 7
Which operation ( +, -, x, ) is attaching the “5” to the “x”?
We must use the Inverse Operation
Operation being used: “+”
Inverse of “+”:
“-”
So we must subtract 5 or add a negative 5 to get the “x” alone in his room.
WE NEED TO GET THE “X” ALONE!
Subtract 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:
X + 5 = 7
Identify who is in the “x” room that shouldn’t be.
Stranger Danger: the “8”x + 8 = 20
Which operation ( +, -, x, ) is attaching the “8” to the “x”?
We must use the Inverse Operation
Operation being used: “+”
Inverse of “+”:
“-”
So we must subtract 8 or add a negative 8 to get the “x” alone in his room.
WE NEED TO GET THE “X” AWAY FROM STRANGER DANGER!
Subtract 8 from each side
On the left, 8 - 8 = 0On the right, 20 - 8 = 12
x + 8 - 8 = 20 - 8
x = 12
Once the “x” is alone on one side,the other side is the answer.
ANSWER:
X + 8 = 20
Identify who is in the “x” room that shouldn’t be.
Stranger Danger: the “9”15 = x - 9
Which operation ( +, -, x, ) is attaching the “9” to the “x”?
We must use the Inverse Operation
Operation being used: “-”
Inverse of “-”:
“+”
So we must add 9 to get the “x” alone in his room.
WE NEED TO GET THE “X” AWAY FROM STRANGER DANGER
Add 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:
15 = X - 9
Multiplication & Division Equations
Identify who is in the “x” room that shouldn’t be.
Stranger Danger: the “2”2x = 16
Which operation ( +, -, x, ) is attaching the “2” to the “x”?
We must use the Inverse Operation
Operation being used: “●”
Inverse of “●”:
“”
So we must divide by 2 to get the “x” alone in his room.
WE NEED TO GET THE “X” AWAY FROM STRANGER DANGER!
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
2X = 16
Identify who is in the “x” room
Stranger Danger: the “2”x = 8
Which operation ( +, -, x, ) is attaching the “2” to the “x”?
We must use the Inverse Operation
Operation being used:
“”
Inverse of “”: “●”
So we must multiply by 2 to get the “x” alone in his room.
2
WE NEED TO GET THE “X” AWAY FROM STRANGER DANGER!
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)
Identify who is in the “x” room
Stranger Danger: the “2/3”2x = 1
Which operation ( +, -, x, ) is attaching the “2/3” to the “x”?
We must use the Inverse Operation
Operation being used: “●”
Inverse of “●”: “÷”
You Cannot Divide FractionsSo we must multiply by the Reciprocal to get the “x” alone in his room.
3
WE NEED TO GET THE “X” AWAY FROM STRANGER DANGER!
2
Multiply each side by 3/2
On the left, 2/3 ● 3/2 = 1 On the right, 1/2 ● 3/2 =
3/4
x = 3/4Once the “x” is alone on one side,
the other side is the answer.
ANSWER:
2x = 1 23
2x = 1 23
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●●
EXIT TICKET1. x + 7 = 39
2. x – 12 = -3
3. 2x = 14
4. = 5
5. x =
x2
25
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