Solve the linear Inequations in R.(3x – 2)/5 ≤ (4x – 3)/2

1.	Solve the linear Inequations in R.(3x – 2)/5 ≤ (4x – 3)/2
Answer» Given as (3x – 2)/5 ≤ (4x – 3)/2 Multiplying both the sides by 5 we get, (3x – 2)/5 × 5 ≤ (4x – 3)/2 × 5 (3x – 2) ≤ 5(4x – 3)/2 3x – 2 ≤ (20x – 15)/2 Multiplying both the sides by 2 we get, (3x – 2) × 2 ≤ (20x – 15)/2 × 2 6x – 4 ≤ 20x – 15 20x – 15 ≥ 6x – 4 20x – 15 + 15 ≥ 6x – 4 + 15 20x ≥ 6x + 11 20x – 6x ≥ 6x + 11 – 6x 14x ≥ 11 Dividing both sides by 14, we get 14x/14 ≥ 11/14 x ≥ 11/14 Therefore, the solution of the given inequation is (11/14, ∞).

Answer»

Given as

(3x – 2)/5 ≤ (4x – 3)/2

Multiplying both the sides by 5 we get,

(3x – 2)/5 × 5 ≤ (4x – 3)/2 × 5

(3x – 2) ≤ 5(4x – 3)/2

3x – 2 ≤ (20x – 15)/2

Multiplying both the sides by 2 we get,

(3x – 2) × 2 ≤ (20x – 15)/2 × 2

6x – 4 ≤ 20x – 15

20x – 15 ≥ 6x – 4

20x – 15 + 15 ≥ 6x – 4 + 15

20x ≥ 6x + 11

20x – 6x ≥ 6x + 11 – 6x

14x ≥ 11

Dividing both sides by 14, we get

14x/14 ≥ 11/14

x ≥ 11/14

Therefore, the solution of the given inequation is (11/14, ∞).

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