Question : If $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$, then the value of $x$ is:
Option 1: $\frac{3}{5}$
Option 2: $-\frac{5}{3}$
Option 3: $\frac{5}{3}$
Option 4: $-\frac{3}{5}$
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Correct Answer: $-\frac{3}{5}$
Solution : Given: $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$ ⇒ $\frac{10x}{3}+(5-\frac{5x}{6})=\frac{7}{2}$ ⇒ $\frac{10x}{3}-\frac{5x}{6}=\frac{7}{2}-5$ ⇒ $\frac{20x-5x}{6}=\frac{7-10}{2}$ ⇒ $\frac{15x}{6}=-\frac{3}{2}$ ⇒ $x=-\frac{3}{5}$ Hence, the correct answer is $-\frac{3}{5}$.
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