Question : If $2x-2(3+4x)<-1-2x>\frac{-5}{3}-\frac{x}{3}$; then $x$ can take which of the following values?
Option 1: 1
Option 2: 2
Option 3: –2
Option 4: –1
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Correct Answer: –1
Solution : Given: $2x-2(3 + 4x) < -1-2x > \frac{- 5}{3}-\frac{x}{3}$ ⇒ $2x-6-8x + 1 + 2x < 0$ and $2x - \frac{x}{3} < -1 + \frac{5}{3}$ ⇒ $-4x-5 < 0$ and $\frac{5x}{3} <\frac{2}{3}$ ⇒ $x > -5/4$ and $x < \frac{2}{5}$ Thus, $- 1.25 < x < 0.4$ From the given options, $x$ can take the value of –1. Hence, the correct answer is –1.
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