3-3 Equations with variables on both sides of the equal sign

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3-3Equations with variables on both sides of the
equal sign
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An equation is like a seesaw.
All the rules for solving equations still apply!
Your goal is to isolate the variable.
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You still undo whatever is being done to the
variable.
You still undo operations by reversing the
order of operationsPEMDAS backwards. (SADMEP)
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• New things to consider when you have a variable
  on both sides of the equal sign
• You must get all the variables onto one side
• You must get all the constants onto the other
  side
• Ex.
• Should I subtract 8x from both sides or subtract
  10x from both sides?

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It doesnt matter which one you choose, but I
like to keep my variable positive if I
can, so I would subtract 8x from both sides.
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Then continue solving as usual.
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Now try some! P. 135 Quick Check 1, a-d Be
careful with b, use must use the distributive
property first!
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Special Cases! 10 8x 2(5-4x) Use the
distributive property. 10 8x 10 8x This
means that for every value of x, this equation is
valid! This is called an identity.
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What if somehow, you didnt notice that both
sides were identical, and kept solving 10 8x
10 8x (add 8x to both sides) 8x
8x 10 10 hopefully, at
this point, you would realize that both sides are
the sameand the answer is identity
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There is one other type 6m - 5 7m 7 m
combine like terms 6m - 5 6m 7
This can never be true!
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If you didnt realize this however, and kept
solving. 6m - 5 6m 7 subtract 6m from
both sides -6m -6m - 5
7 This can never be true! The answer to this type
of problem is no solution.
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Now you can start your homework! p. 136-137 1-12
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