Solve the given inequality for real x : 3(x - 1) ≤ 2 (x - 3)

3(x - 1) ≤ 2 (x - 3)

⇒ 3x - 3 ≤ 2x - 6

⇒ 3x - 3 + 3 ≤ 2x - 6 + 3

⇒ 3x ≤ 2x - 3

⇒ 3x - 2x ≤ 2x - 3 - 2x

⇒ x ≤ - 3

Thus, all real numbers x,

which are less than or equal to - 3, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (- ∞, - 3]

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 7

Solve the given inequality for real x : 3(x - 1) ≤ 2 (x - 3)

Summary:

A linear inequation 3(x - 1) ≤ 2 (x - 3) is given. We have found that the solution set of the given inequality is (- ∞, - 3]