Solve the linear Inequations in R.[2(x - 1)]/5 ≤ [3(2 + x)]/7

1.	Solve the linear Inequations in R.[2(x - 1)]/5 ≤ [3(2 + x)]/7
Answer» Given as [2(x - 1)]/5 ≤ [3(2 + x)]/7 (2x – 2)/5 ≤ (6 + 3x)/7 Multiplying both the sides by 5 we get, (2x – 2)/5 × 5 ≤ (6 + 3x)/7 × 5 2x – 2 ≤ 5(6 + 3x)/7 7(2x – 2) ≤ 5(6 + 3x) 14x – 14 ≤ 30 + 15x 14x – 14 + 14 ≤ 30 + 15x + 14 14x ≤ 44 + 15x 14x – 44 ≤ 44 + 15x – 44 14x – 44 ≤ 15x 15x ≥ 14x – 44 15x – 14x ≥ 14x – 44 – 14x x ≥ –44 Therefore, the solution of the given inequation is [–44, ∞).

Answer»

Given as

[2(x - 1)]/5 ≤ [3(2 + x)]/7

(2x – 2)/5 ≤ (6 + 3x)/7

Multiplying both the sides by 5 we get,

(2x – 2)/5 × 5 ≤ (6 + 3x)/7 × 5

2x – 2 ≤ 5(6 + 3x)/7

7(2x – 2) ≤ 5(6 + 3x)

14x – 14 ≤ 30 + 15x

14x – 14 + 14 ≤ 30 + 15x + 14

14x ≤ 44 + 15x

14x – 44 ≤ 44 + 15x – 44

14x – 44 ≤ 15x

15x ≥ 14x – 44

15x – 14x ≥ 14x – 44 – 14x

x ≥ –44

Therefore, the solution of the given inequation is [–44, ∞).

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