The integral solutions of the inequality $5 x - 1 < (x + 1)^{2} < 7 x - 3$ are

3, 4

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2, 3

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3

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2, 3, 4

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Solution

The correct option is B $3$
We have,
$x^{2} + 2 x + 1 > 5 x - 1$
$\Rightarrow x^{2} - 3 x + 2 > 0$
$\Rightarrow (x - 2) (x - 1) > 0$
$\Rightarrow x > 2$ or $x < 1$
Also,
$x^{2} + 2 x + 1 < 7 x - 3$
$\Rightarrow (x - 4) (x - 1) < 0$
$\Rightarrow 1$
The common set of both the inequalities is $2$
Hence, the only integral value $x$ can take is 3.

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