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Question
`(2x + 3)/(3) ≥ (3x - 1)/(4)` where x is positive even integer.
Solution
`(2x + 3)/(3) ≥ (3x - 1)/(4)`
⇒ `(2x)/(3) + (3)/(3) ≥ (3x)/(4) - (1)/(4)`
⇒ `(2x)/(3) - (3x)/(4) ≥ (-1)/(4) - 1`
⇒ `(8x - 9x)/(12) ≥ - (5)/(4)`
⇒ `(-x)/(12) ≥ (-5)/(4)`
⇒ `x/(12) ≤ (5)/(4)`
⇒ `x ≤ (5)/(4) xx 12`
⇒ x ≤ 15
∵ x is positive even integer
∴ x = {2, 4, 6, 8, 10, 12, 14}.
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