Find the number of integral values of x for which

(5x - 1) < (x + 1)2 < (7x – 3)

- 1
- 2
- 3
- 4

Option 1 : 1

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**Calculation:**

Taking

⇒ (x + 1)^{2 }> (5x - 1)

⇒ x^{2} – 3x + 2 > 0

⇒ (x – 1 )( x – 2 ) > 0

X < 1 or x > 2 ……(i)

Taking

⇒ (x + 1)^{2} < (7x – 3)

⇒ x^{2} – 5x + 4 > 0

⇒ (x – 1 )( x – 4 ) > 0

⇒ 1 < x < 4 ……(ii)

Combining (1) and (2) we get 2 < x < 4

Hence, x will only take one integer i.e. **3**

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