Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?
Option 1: –$10$
Option 2: $\frac{9}{8}$
Option 3: $10$
Option 4: $–\frac{9}{8}$
Correct Answer: $10$
Solution :
$\frac{x}{2}–\frac{\left [4\left ( \frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$
⇒ $\frac{x}{2}+\frac{x}{18} = \frac{\left [ 4\left ( \frac{15}{2}-\frac{x}{3} \right )\right ]}{3}$
⇒ $\frac{20x}{36} = \frac{30–\frac{4x}{3}}{3}$
⇒ $\frac{5x}{9} = 10-\frac{4x}{9}$
⇒ $\frac{5x}{9}+\frac{4x}{9} = 10$
$\therefore x =10$
Hence, the correct answer is $10$.
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