Linear Inequations-2

Solve the inequations:
(i)(2x - 3)/4 + 9 ≥ 3 + 4x/3
(ii) (5x - 2)/3 – (7x - 3)/ 5 > x/4

Solution: (i) We have, (2x - 3)/4 + 9 ≥ 3 + 4x/3

=>(2x - 3)/4 – 4x/3 ≥ 3 – 9 [Transposing 4x/3 to LHS and 9 to RHS]

=> [3(2x - 3) – 16x]/12 ≥ -6

=> (6x – 9 – 16x)/12 ≥ -6

=> (-9 – 10x)/12 ≥ -6

=> -9 – 10x ≥ -72 [Multiplying both sides by 12]

=> -10x ≥ -72 + 9

=> -10x ≥ -63

=>-10x/-10 ≤ -63/-10

=> x ≤ 63/10

=> x ∈ (-∞, 63/10]

Hence, the solution set of the given inequation is (-∞, 63/10].

(ii) We have, (5x - 2)/3 – (7x - 3)/ 5 > x/4

=>[5(5x - 2) – 3(7x - 3)]/15 >x/4

=> (25x – 10 – 21x + 9)/15 > x/4

=> (4x - 1)/15 > x/4

=> 4(4x - 1) > 15x [Multiplying both sides by 60 i.e. LCM of 15 and 4]

=>16x – 15x > 4 [Transposing 15x to LHS and -4 to RHS]

=> x > 4

=> x ∈ (4, ∞)

Hence, the solution set of the given inequation is (4, ∞).