What is the value of \( b \)?
\[\frac{1}{3}(2b + 9) = \frac{2}{3}\left(b + \frac{9}{2}\right)\]
Answer (2)
3 1 ( 2 b + 9 ) = 3 2 ( b + 2 9 ) ∣ m u lt i pl y b y 3 2 b + 9 = b + 2 9 ∣ m u lt i pl y b y 2 4 b + 18 = 2 b + 9 ∣ s u b t r a c t 2 b 2 b + 18 = 9 ∣ s u b t r a c t 18 2 b = − 9 ∣ d i v i d e b y 2 b = − 4 , 5
The equation 3 1 ( 2 b + 9 ) = 3 2 ( b + 2 9 ) simplifies down to an identity, indicating that b can take any value. Both sides of the original equation are equal, making b unrestricted. Solutions by specific substitutions yield satisfying results confirming the values.
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