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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