Question : If $2+4x<5-\frac{x}{2}$ and $3x+3>-5-3x$, 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: $2+4x<5-\frac{x}{2}$ and $3x+3>-5-3x$
Or, $2+4x<\frac{10-x}{2}$ and $3x+3x>-5-3$
Or, $2(2+4x)<10-x$ and $6x>-8$
Or, $4+8x<10-x$ and $x>\frac{-8}{6}$
Or, $x+8x<10-4$ and $x>\frac{-4}{3}$
Or, $9x<6$ and $x>-1.33$
Or, $x<\frac{6}{9}$ and $x>-1.33$
Or, $x<0.67$ and $x>-1.33$
Or, $-1.33<x<0.67$
Amongst all the given values –1 satisfies the above condition.
Hence, the correct answer is –1.
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