Solve the given inequality for real x : x/4 < (5x - 2)/3 - (7x - 3)/5

Solution:

x/4 < (5x - 2)/3 + (7x - 3)/5

⇒ x/4 < [5(5x - 2) - 3(7x - 3)]/15

⇒ x/4 < [25x - 10 - 21x + 9]/3

⇒ x/4 < (4x - 1)/15

⇒ 15x < 4(4x - 1)

⇒ 15x < 16x - 4

⇒ 4 < 16x - 15x

⇒ x > 4

Thus, all real numbers x,

which are greater than 4, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (4, ∞)

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 15

Solve the given inequality for real x : x/4 < (5x - 2)/3 + (7x - 3)/5

Summary:

A linear inequation x/4 < (5x - 2)/3 + (7x - 3)/5 is given. We have found that the solution set of the given inequality is (4, ∞)