Solve the perimeter formula for an isosceles triangle, P=2a+b, for b @AccessDenied

Question

accessdenied · Answer

P = 2a + b
We want to solve for b.  Our goal is isolating b on one side of the equation, moving the other variables to the opposite side.
So, what operation cancels the addition of 2a?

anonymous · Answer

division

anonymous · Answer

a. 2a/p b. b=p-2a c. b=p+2a d. b= p/2a

accessdenied · Answer

Ah, not division.  Multiplication and division are inverse operations.  The inverse operation of addition is actually subtraction.  Since if we add and subtract the same number, the end result is 0.  Just like if we multiply and divide by the same number, the result is 1.

We want to subtract 2a from both sides so that:
  P - 2a = 2a + b - 2a    <-- the right side 2a and -2a add to 0.  That makes sense?

anonymous · Answer

yes

accessdenied · Answer

Upon performing that operation:
  $ P -2a = \cancel{2a} + b \cancel{- 2a} $
This leaves b on the right-side.
  $ P - 2a = b $
We can flip this equality around because a=b and b=a are the same statement.  That will be one of your answer choices.  :)

anonymous · Answer

can i do P/2=2a/2+b?

accessdenied · Answer

Because we are not interested in the a at all -- we are only interested in moving things away from b --, we don't have to do anything about the 2a term.  If we divide both sides by 2, we start complicating the equation for b.

Also, if we multiply or divide both sides, everything has to be multiplied or divided:
  $ a  =  b + c$ 
  $ 2* a = 2* (b+c)$

accessdenied · Answer

If we divide by 2:
  $ P = 2a + b $
  $ P/2 = (2a + b) / 2 $
  $ P/2 = a + b/2 $   <-- but now our b has a coefficient which we cannot have by solving for b.

anonymous · Answer

thanks for your help. :)

accessdenied · Answer

Glad to help.  :)

anonymous · Answer

ok