find the common solution of (X - 7) (x -15 is less than 0 and (x-2) (x-8) (x-2) l is greater than or equal to 0
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Step-by-step explanation:
`log_0.5 ((3-x)/(x+2)) lt 0`
Here, `((3-x)/(x+2))` should be greater than `0` as we can not have logarithms of negative values.
`:. (3-x)/(x+2) gt 0`
`=>x !=-2 and x lt 3`
`=> x in (-2,3) ->(1)`
Now, `log_0.5 ((3-x)/(x+2)) lt 0`
`=> (3-x)/(x+2) lt 0^(0.5)`
`=> (3-x)/(x+2) lt 1`
`=> (3-x)/(x+2) - 1 lt 0`
`=> (3-x-x-2)/(x+2) lt 0`
`=>(1-2x)/(x+2) lt 0`
`:. x in (-oo,-2)->(2)`
From (1) and (2), we can see that their is no common value that lies in both intervals.
So, there is no solution available for the given solution.
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