Linear Inequations-3

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Solve the following inequations:
(i)1/2 (3x/5 + 4) ≥ 1/3 (x - 6)
(ii) 3(x - 2)/5 ≥ 5(2 – x)/3

Solution: (i) We have, 1/2 (3x/5 + 4) ≥ 1/3 (x - 6)

=>1/2 [(3x + 20)/5] ≥ 1/3 (x - 6)

=> (3x + 20)/10 ≥ (x - 6)/3

=> 3(3x + 20) ≥ 10(x - 6) [Multiplying both sides by 30 i.e. LCM of 3 and 10]

=> 9x + 60 ≥ 10x – 60

=> 9x – 10x ≥ -60 -60

=> -x ≥ -120

=> x ≤ 120 [Multiplying both sides by -1]

=> x ∈ (-∞, 120]

Hence, the solution set of the given inequation is (-∞, 120].

(ii) We have,

3(x - 2)/5 ≥ 5(2 – x)/3

=>(3x – 6)/5 ≥ (10 – 5x)/3

=> 3(3x - 6) ≥ 5(10 - 5x) [Multiplying both sides by 15, the LCM of 5 and 3]

=> 9x – 18 ≥ 50 – 25x

=> 9x + 25x ≥ 50 + 18 [Transposing -25x to LHS and 18 to RHS]

=> 34x ≥ 68

=> 34x/34 ≥ 68/34

=> x ≥ 2

=> x ∈ [2, ∞)

Hence, the solution set of the given inequation is [2, ∞).

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