SOLUTION: Given the following equality: g(x) + g(x + 3) = 2x + 5 And: g(2) + g(8) = 12 Find: g(5) Thanks

Question 1206208: Given the following equality:
g(x) + g(x + 3) = 2x + 5
And:
g(2) + g(8) = 12
Find:
g(5)
Thanks
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.
Given the following equality:
g(x) + g(x + 3) = 2x + 5
And:
g(2) + g(8) = 12
Find g(5).
~~~~~~~~~~~~~~~~~~~~~

Take x= 2. Then from the formula g(x) + g(x + 3) = 2x + 5 you have

    g(2) + g(5) =  9.    (1)


Take x= 5. Then from the formula g(x) + g(x + 3) = 2x + 5 you have

    g(5) + g(8) = 15.    (2)


Add equations (1) and (2).  You will get

    g(2) + 2*g(5) + g(8) = 24.


Replace here g(2) + g(8) by 12 (since it is given in the problem).  You will get

    12 + 2*g(5) = 24  --->  2*g(5) = 24-12 = 12  --->  g(5) = 12/2 = 6.


ANSWER.  g(5) = 6.

Solved.

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