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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