Solve the linear Inequations in R.(2x + 3)/4 – 3 < (x – 4)/3 – 2

1.	Solve the linear Inequations in R.(2x + 3)/4 – 3 < (x – 4)/3 – 2
Answer» Given as (2x + 3)/4 – 3 < (x – 4)/3 – 2 Adding 3 on both sides we get, (2x + 3)/4 – 3 + 3 < (x – 4)/3 – 2 + 3 (2x + 3)/4 < (x – 4)/3 + 1 (2x + 3)/4 < (x – 4 + 3)/3 (2x + 3)/4 < (x – 1)/3 On cross multiply we get, 3(2x + 3) < 4(x – 1) 6x + 9 < 4x – 4 6x + 9 – 9 < 4x – 4 – 9 6x < 4x – 13 6x – 4x < 4x – 13 – 4x 2x < –13 Dividing both sides by 2, we get 2x/2 < -13/2 x < -13/2 Therefore, the solution of the given inequation is (-∞, -13/2).

Answer»

Given as

(2x + 3)/4 – 3 < (x – 4)/3 – 2

Adding 3 on both sides we get,

(2x + 3)/4 – 3 + 3 < (x – 4)/3 – 2 + 3

(2x + 3)/4 < (x – 4)/3 + 1

(2x + 3)/4 < (x – 4 + 3)/3

(2x + 3)/4 < (x – 1)/3

On cross multiply we get,

3(2x + 3) < 4(x – 1)

6x + 9 < 4x – 4

6x + 9 – 9 < 4x – 4 – 9

6x < 4x – 13

6x – 4x < 4x – 13 – 4x

2x < –13

Dividing both sides by 2, we get

2x/2 < -13/2

x < -13/2

Therefore, the solution of the given inequation is (-∞, -13/2).

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