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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