Solve the given inequality for real x : 3( x - 2)/5 ≤ 5(2 - x)/3

Solution:

3( x - 2)/5 ≤ 5(2 - x)/3

⇒ 9( x - 2) ≤ 25(2 - x)

⇒ 9x - 18 ≤ 50 - 25x

⇒ 9x + 25x ≤ 50 + 18

⇒ 34x ≤ 68

⇒ x ≤ 68/34

⇒ x ≤ 2

Thus, all real numbers x,

which are less than or equal to 2, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (- ∞, 2]

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 11

Solve the given inequality for real x : 3( x - 2)/5 ≤ 5(2 - x)/3

Summary:

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