Question

Find $v$, if $\frac{3v}{8}-5v=-3(\frac{8}{9}+6v)+12v$.

• A. $\frac{-64}{33}$
• B. $\frac{64}{33}$
• C. $\frac{33}{64}$
• D. $\frac{-33}{64}$

Answer 1

Answer: (A)

$\frac{-64}{33}$

Given, $\frac{3v}{8}-5v=-3(\frac{8}{9}+6v)+12v$

$\Rightarrow \frac{3v-40v}{8}=\frac{-24}{9}-18v+12v$ ...[Simplifying]

$\Rightarrow \frac{-37v}{8}=\frac{-24}{9}-6v$

$\Rightarrow \frac{-37v}{8}=\frac{-8}{3}-6v$.

Transposing $v$ terms to one side, we get,

$\Rightarrow \frac{-37v}{8}+6v=\frac{-8}{3}$

$\Rightarrow \frac{-37v+48v}{8}=\frac{-8}{3}$ ....[Simplifying]

$\Rightarrow \frac{11v}{8}=\frac{-8}{3}$

$\Rightarrow v=\frac{-64}{33}$.

Hence, option $A$ is correct.