Question

Which of the following is not a linear inequation?

Options

• 3x – 8 > 5 + 2x

• `5/2x - 3 ≤ 9/4x + 12`

• `4x - 7/3 ≥ 13x + 8`

• `6x + 13 < 4/x - 3`

Answer 1

`bb(6x + 13 < 4/x - 3)`

Explanation:

Solving, option 4:

⇒ `6x + 13 < 4/x - 3`

⇒ `6x + 13 < (4 - 3x)/x`

Case 1: If x is positive,

⇒ x(6x + 13) < 4 – 3x

⇒ 6x² + 13x < 4 – 3x

⇒ 6x² + 13x + 3x < 4

⇒ 6x² + 16x < 4

Case 2: If x is negative,

⇒ x(6x + 13) > 4 – 3x

⇒ 6x² + 13x > 4 – 3x

⇒ 6x² + 13x + 3x > 4

⇒ 6x² + 16x > 4

Since, the highest power of x is 2.

∴ `6x + 13 < 4/x - 3` is not linear.