Question

Which of the following is not reducible to a linear inequation?

विकल्प

• `3 - 7/x < 5`

• `8 + 3/x ≥ 5/x - 4`

• `6/x - 8 > 4/x + 3x`

• `3/(x - 1) - 7 < 9`

Answer 1

`bb(6/x - 8 > 4/x + 3x)`

Explanation:

Solving option 3,

⇒ `6/x - 8 > 4/x + 3x`

⇒ `(6 - 8x)/x > (4 + 3x^2)/x`

Case 1: If x is positive,

⇒ 6 – 8x > 4 + 3x²

⇒ 4 + 3x² < 6 – 8x

⇒ 3x² + 8x < 6 – 4

⇒ 3x² + 8x < 2

Case 2: If x is negative,

⇒ 6 – 8x < 4 + 3x²

⇒ 4 + 3x² > 6 – 8x

⇒ 3x² + 8x > 6 – 4

⇒ 3x² + 8x > 2

Since, the highest power of x is 2 in both the cases,

`6/x - 8 > 4/x + 3x` is not reducible to linear inequation.