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

Solution:

(2x - 1)/3 ≥ (3x - 2)/4 - (2 - x)/5

⇒ (2x - 1)/3 ≥ [5(3x - 2) - 4 (2 - x)]/20

⇒ (2x - 1)/3 ≥ [15x - 10 - 8 + 4x]/20

⇒ (2x - 1)/3 ≥ (19x - 18)/20

⇒ 20 (2x - 1) ≥ 3(19x - 18)

⇒ 40x - 20 ≥ 57x - 54

⇒ 40x - 57x ≥ 20 - 54

⇒ - 17x ≥ - 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]

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NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 16

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

Summary:

A linear inequation (2x - 1)/3 ≥ (3x - 2)/4 - (2 - x)/5 is given. We have found that the solution set of the given inequality is (- ∞, 2]