Question : If $\frac{5}{2}-\left (\frac{6}{5}\right )\left (x-\frac{15}{2} \right)=\frac{-x}{5}$, then what is the value of $x$?
Option 1: $-\frac{23}{2}$
Option 2: $\frac{13}{2}$
Option 3: $-\frac{13}{2}$
Option 4: $\frac{23}{2}$
Correct Answer: $\frac{23}{2}$
Solution :
Given equation:
$\frac{5}{2}-\left (\frac{6}{5} \right )\left (x-\frac{15}{2}\right) =\frac{-x}{5}$
⇒ $\frac{5}{2}-\frac{6x}{5}+9=\frac{-x}{5}$
⇒ $\frac{5}{2} + 9=\frac{-x}{5} +\frac{6x}{5}$
⇒ $\frac{23}{2}=\frac{5x}{5}$
⇒ $x = \frac{23}{2}$
Hence, the correct answer is $\frac{23}{2}$.
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