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 : Expression 1: $2x-3(4-2x)<4x-5$ $⇒ 2x - 12 + 6x <4x-5$ $⇒ 8x - 12 < 4x - 5$ $⇒ 4x - 12 < -5$ $⇒ 4x < 7$ $⇒ x < \frac{7}{4}$ Expression 2: $4x-5<4x+\frac{2x}{3}$ $⇒ -5 < \frac{2x}{3}$ $⇒ -15 < 2x$ $⇒ x > -\frac{15}{2}$ So, the solution to the inequalities is $-\frac{15}{2} < x < \frac{7}{4}$. Hence, the correct answer is 0.
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