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Question
Solve the inequation : `(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7), x ∈ "R"`
Solution
`(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7)`
`(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ (8)/(5) + (3x - 1)/(7)`
Multiplying by L.C.M. of 7 and 5 i.e. 35
25x + 5 - 4 (5x + 14) ≤ 56 + 15x - 5
25x + 5 - 20x - 56 ≤ 56 - 5 - 5 + 56
25x - 20x - 15x ≤ 56 - 5 - 5 + 56
-10x ≤ 102
-x ≤`(102)/(10)`
⇒ -x ≤ `(51)/(5)`
⇒ x ≥ - `(51)/(5)`
∵ x ∈ R
∴ Solution set = `{x : x ∈ "R", x ≥ - (51)/(5)}`
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