Question : If $4(2x+3)>5-x$ and $5x-3(2x-7)>3x-1,$ then $x$ can take which of the following values?
Option 1: 6
Option 2: –1
Option 3: 5
Option 4: –6
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Correct Answer: 5
Solution :
The first inequality:
$4(2x+3)>5-x$
$⇒8x+12>5-x$
$⇒9x>-7$
$⇒x>-\frac{7}{9}$
The second inequality:
$5x-3(2x-7)>3x-1$
$⇒5x-6x+21>3x-1$
$⇒-4x> -22$
$⇒4x<22$
$⇒x<\frac{22}{4}$
$⇒x<5.5$
$\therefore$ The solution to the inequalities is $-\frac{7}{9} < x < 5.5$.
Hence, the correct answer is 5.
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