Solve the linear Inequations in R.(x – 1)/3 + 4 < (x – 5)/5 – 2

1.	Solve the linear Inequations in R.(x – 1)/3 + 4 < (x – 5)/5 – 2
Answer» Given as (x – 1)/3 + 4 < (x – 5)/5 – 2 Subtracting both sides by 4 we get, (x – 1)/3 + 4 – 4 < (x – 5)/5 – 2 – 4 (x – 1)/3 < (x – 5)/5 – 6 (x – 1)/3 < (x – 5 – 30)/5 (x – 1)/3 < (x – 35)/5 On cross multiply we get, 5(x – 1) < 3(x – 35) 5x – 5 < 3x – 105 5x – 5 + 5 < 3x – 105 + 5 5x < 3x – 100 5x – 3x < 3x – 100 – 3x 2x < –100 Dividing both sides by 2, we get 2x/2 < -100/2 x < -50 Therefore, the solution of the given inequation is (-∞, -50).

Answer»

Given as

(x – 1)/3 + 4 < (x – 5)/5 – 2

Subtracting both sides by 4 we get,

(x – 1)/3 + 4 – 4 < (x – 5)/5 – 2 – 4

(x – 1)/3 < (x – 5)/5 – 6

(x – 1)/3 < (x – 5 – 30)/5

(x – 1)/3 < (x – 35)/5

On cross multiply we get,

5(x – 1) < 3(x – 35)

5x – 5 < 3x – 105

5x – 5 + 5 < 3x – 105 + 5

5x < 3x – 100

5x – 3x < 3x – 100 – 3x

2x < –100

Dividing both sides by 2, we get

2x/2 < -100/2

x < -50

Therefore, the solution of the given inequation is (-∞, -50).

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