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The solution of the inequality ((x+7)/(x...

The solution of the inequality `((x+7)/(x-5)+(3x+1)/(2) )ge 0 ` is

A

a. `[1,3] cup (5,oo)`

B

b. `(1,3) cup (5,oo)`

C

c. `(-oo,1) cup (5,oo)`

D

d. None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have `(x+7)/(x-5)+(3x+1)/(2) ge 0 `
`rArr (2x+14 +3x^2-14x-5)/(2(x-5)) ge 0 `
`rArr (3x^2-12x+9)/(2(x-5)) le 0 `
`rArr ((x-1)(x-3))/(x-5) ge 0 `

Form the sign scheme , `x in [1,3]cup (5,oo)`
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