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