Solve the given inequality for real x : 1/2 (3x/5 + 4) ≥ 1/3 (x - 6)

Solution:

1/3 (3x/5 + 4) ≥ 1/3 (x - 6)

⇒ 3 (3x/5 + 4) ≥ 2 (x - 6)

⇒ (9x + 5)/12 ≥ 2x - 12

⇒ 12 + 12 ≥ 2x - 9x/5

⇒ 24 ≥ (10x - 9x)/5

⇒ 24 ≥ x/5

⇒ x ≤ 120

Thus, all real numbers x,

which are less than or equal to 120, are the solutions of the given inequality

Hence, the solution set of the given inequality is (- ∞, 120]

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 12

Solve the given inequality for real x : 1/3 (3x/5 + 4) ≥ 1/3 (x - 6)

Summary:

A linear inequation 1/3 (3x/5 + 4) ≥ 1/3 (x - 6) is given. We have found that the solution set of the given inequality is (- ∞, 120]