Question

Solve the following linear inequations in R 

(6x-5)/(4x+1) < 0

\(\frac{6x-5}{4x+1}\)< 0 

Answer 1

Given,

(6x-5)/(4x+1) < 0

For this inequation to be true,

There are two possible cases. 

i. 6x – 5 > 0 and 4x + 1 < 0 

⇒ 6x – 5 + 5 > 0 + 5 and 

4x + 1 – 1 < 0 – 1 

⇒ 6x > 5 and 4x < –1

Hence,

This case is not possible.

ii. 6x – 5 < 0 and 4x + 1 > 0

⇒ 6x – 5 + 5 < 0 + 5 and 

4x + 1 – 1 > 0 – 1 

⇒ 6x < 5 and 4x > –1

Thus,

The solution of the given inequation is (\(-\frac{1}{4}\),\(\frac{5}{6}\)).