Download Solving Two-Step Equations

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Algebra 1 Notes
Solving Two-Step Equations
Essential Question: How do you solve equations, and what do you undo first?
Solve:
to find the value(s) of the variable that make the equation true
To solve an equation, you have to undo what has been done to the variable to
get the variable by itself.
(
)
– a coefficient of positive one
(To undo something, you work _backwards_) *undo = reverse P E MD AS order
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The Goal:
Get the ___variable___ you are solving for on ___one side___ of the equation
____by itself____ with a coefficient of ____positive one_____.
How? Main Idea:
Ex. _X =_#_
Identify _____what is with the variable_______, how it is ____held there_____
(by addition, subtraction, multiplication, or division) and ___do the opposite___
to get rid of it – if it is held there by addition or subtraction, you will have to do
one of the two (addition or subtraction) to get rid of it – whichever one makes it
go away. Use…
Inverse operations:
(Opposite)
__Addition__ & ___Subtraction____; __Multiplication___ & __Division___
* Always do the __same thing__ to __both sides___ of the equation,
but only ___once____ on ___each side____.
Property of
Equality:
Whatever you do to one side of an equation you must also do to the other side
of the equation so that they stay equal.
Steps to Solve:
1. __Distribute___ to get rid of __any parenthesis__.
(DCMI)
2. __Combine__ __like__-_terms_ on each side of the equation __separately__
*Do not combine like-terms across the equal sign. Do step three for those.
3. __Move__ all terms with the __variable__ you are solving for to __one side__
of the equation and everything else to __the other side___.
(Use _+_ /_–_)
4. __Isolate__ the variable – Get the __variable__ you are solving for _by itself_
with a coefficient of _1_. (Use _×_ /_÷_)
5. You can always check your answer by plugging it in to the original equation.
Practice:
Solve each equation.
*Remember: To solve two-step equations (equations with addition/subtraction
and multiplication/division) work in reverse PEMDAS order.
*addition and subtraction first – then multiplication and division
Summary
Always undo addition and subtraction before
multiplication and division.
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