Part I : 5x + 2 < 3x + 8.
⇒ 2x < 6
⇒ x < 3
Part II : (x+2)/(x-1) < 4.
⇒ \(\frac{x+2}{x-1}\) - 4 < 0
⇒ \(\frac{(x+2)-4(x-1)}{x-1}\)< 0
⇒ \(\frac{-3x+6}{x-1}\) < 0
Case I : - 3x + 6 < 0 and x – 1 > 0
⇒ x > 2 and x > 1
By taking intersection x ∈ (2, ∞)
Case II : - 3x + 6 > 0 and x – 1 < 0
⇒ x < 2 and x < 1
By takin intersection x ∈ (-∞, 1)
Taking union of case I and case II,
x ∈ (-∞, 1) (2, ∞)
We have to take intersection of part I and part II,
We have final answer i.e.,
x ∈ (-∞, 1) (2, 3)
