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Solve (x-1 )(x-2)(1-2x) gt 0...

Solve `(x-1 )(x-2)(1-2x) gt 0`

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We have `(x-1 )(x-2)(1-2x) gt 0`
`-(x-1)(x-2)(2x-1) gt 0 `
or ` (x-1)(x-2)(2x-1)lt 0` On the number line mark x=1/2, 1,2

When `x gt 2` all factors (x-1),(2x-1)and (x-2) are positive .
Hence` (x-1)(x-2)(2x-1) gt 0 for x gt 2 .`
Now put positive and negative signs alternatively as shown in the figure
Hence , solution set of `(x-1)(x-2)(1-2x) lt is (- oo , 1//2 ) cup (1,2)`
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