Question : Simplify the following.
$\frac{3 a+b}{2}-\frac{a-3 b}{3}+2b$
Option 1: $\frac{5(a+3b)}{6}$
Option 2: $\frac{7a+3b}{6}$
Option 3: $\frac{7(a+3b)}{6}$
Option 4: $\frac{a+3b}{6}$
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Correct Answer: $\frac{7(a+3b)}{6}$
Solution :
Given: $\frac{3a+b}{2}-\frac{a-3b}{3}+2b$
= $\frac{9a+3b-(2a-6b)}{6}+2b$
= $\frac{7a+9b}{6}+2b$
= $\frac{7a+9b + 12b}{6}$
= $\frac{7a+21b }{6}$
= $\frac{7(a+3b) }{6}$
Hence, the correct answer is $\frac{7(a+3b) }{6}$.
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