Question 223968
My son's homework question is:

Find the value(s) of a for which the equation is an identity.

a(2x+3) = 9x + 12 - x

What exactly are they asking him to do here?  I don't understand what they are looking for.  Should he solve for a, or for x in terms of a?

thanks,
Andrea


a(2x + 3) = 9x + 12 - x


a(2x + 3) = 9x - x + 12


a(2x + 3) = 8x + 12


a(2x + 3) = 4(2x + 3)


As seen, there is a common factor on each side of equation, and that common factor is 2x + 3


As can be seen also, "a" MUST equal 4. 


If this is still unclear, let's consider the following:


b(2 + 1) = 5(2 + 1). We're supposed to get "b" = 5.


Let's go the long way.


b(2 + 1) = 5(2 + 1)


2b + b = 5(3)


3b = 15

{{{b = 15/3 = 5}}}


Therefore, as stated previously, {{{highlight_green(a = 4)}}}