Question : If $2x-3(4-2x)<4x-5<4x+\frac{2x}{3}$, then $x$ can take which of the following values?
Option 1: 2
Option 2: 8
Option 3: 0
Option 4: –8
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Correct Answer: 0
Solution : Given: $2x-3(4-2x)<4x-5<4x+\frac{2x}{3}$ $⇒2x-12+6x<4x-5<4x+\frac{2x}{3}$ Now, taking the first part of the inequality, we get, $2x-12+6x<4x-5$ $⇒8x - 12 < 4x - 5$ $⇒8x - 4x - 12 < -5$ $⇒x < \frac{7}{4}$ Also, $4x - 5 < 4x + (\frac{2x}{3})$ $⇒-5 < (\frac{2x}{3})$ $⇒-15 < 2x$ $⇒x > \frac{-15}{2}$ $⇒x > -7.5$ So, the range of $x$ is $-7.5 < x < 1.75$. Hence, the correct answer is 0.
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